Finite Group Databasebeta

← C47×#14725 #26054423

Subgroups — C47×#14725 #26054423

Order 12032.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C47C211yesmaximal, characteristic
2C23×C22⋊C4×C47C211yesmaximal, characteristic, complemented
3C2×C47×#394C212yesmaximal, complemented
4C2×C47×#386C211yesmaximal, characteristic, complemented
5C2×C47×#386C211yesmaximal, characteristic, complemented
6C2×C47×#380C211yesmaximal, characteristic, complemented
7C2×C47×#379C211yesmaximal, characteristic, complemented
8C47×#1440C212yesmaximal, complemented
9C47×#1439C212yesmaximal, complemented
10C47×#1438C212yesmaximal, complemented
11C47×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C47C2211yescharacteristic
13C23×D4×C47C2211yescharacteristic
14C23×D4×C47C2212yes—
15C24×C4×C47C2211yescharacteristic
16C24×C4×C47C2211yescharacteristic
17C2×#120×C47—24no—
18C2×#120×C47—24no—
19C2×#120×C47—24no—
20C22×C4⋊C4×C47C2212yescomplemented
21C22×C22⋊C4×C47—24no—
22C22×C22⋊C4×C47—28no—
23C22×C22⋊C4×C47C2211yescharacteristic
24C22×C22⋊C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47C2212yes—
26C22×C22⋊C4×C47C2212yes—
27C22×C22⋊C4×C47C2212yes—
28C22×C22⋊C4×C47C2211yescharacteristic
29C22×C22⋊C4×C47C2212yes—
30C22×C22⋊C4×C47C2212yes—
31C22×C22⋊C4×C47C2211yescharacteristic, complemented
32C22×C22⋊C4×C47C2212yescomplemented
33C22×C22⋊C4×C47C2211yescharacteristic, complemented
34C47×#394—28no—
35C47×#386—24no—
36C47×#386—24no—
37C47×#380—24no—
38C47×#379—24no—
39C2×#95×C47C2212yescomplemented
40C2×#95×C47C2211yescharacteristic, complemented
41C2×#95×C47C2212yescomplemented
42C2×#95×C47C2211yescharacteristic, complemented
43C2×#95×C47C2212yescomplemented
44C2×#95×C47C2212yescomplemented
45C25×C47—24no—
46C25×C47—22no—
47C25×C47—24no—
48C25×C47—22no—
49C25×C47—22no—
50C25×C47—22no—
51C25×C47—22no—
52C25×C47—22no—
53C25×C47—42no—
54C25×C47—42no—
55C25×C47D414yes—
56C25×C47C2311yescharacteristic
57C25×C47C2312yes—
58C25×C47C2311yescharacteristic
59C22×D4×C47—24no—
60C22×D4×C47—24no—
61C22×D4×C47—22no—
62C22×D4×C47—22no—
63C22×D4×C47—22no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—24no—
68C22×D4×C47—24no—
69C22×D4×C47—24no—
70C22×D4×C47—42no—
71C22×D4×C47—42no—
72C22×D4×C47D414yes—
73C23×C4×C47—22no—
74C23×C4×C47—22no—
75C23×C4×C47—22no—
76C23×C4×C47—24no—
77C23×C4×C47—24no—
78C23×C4×C47—22no—
79C23×C4×C47—22no—
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×C47C2311yescharacteristic
88C23×C4×C47C2312yes—
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91#120×C47—232no—
92C2×C4⋊C4×C47—24no—
93C2×C4⋊C4×C47—24no—
94C2×C4⋊C4×C47—42no—
95C2×C22⋊C4×C47—232no—
96C2×C22⋊C4×C47—24no—
97C2×C22⋊C4×C47—24no—
98C2×C22⋊C4×C47—22no—
99C2×C22⋊C4×C47—22no—
100C2×C22⋊C4×C47—24no—
101C2×C22⋊C4×C47—24no—
102C2×C22⋊C4×C47—24no—
103C2×C22⋊C4×C47—24no—
104C2×C22⋊C4×C47—24no—
105C2×C22⋊C4×C47—24no—
106C2×C22⋊C4×C47—24no—
107C2×C22⋊C4×C47—22no—
108C2×C22⋊C4×C47—24no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—22no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47—24no—
114C2×C22⋊C4×C47—24no—
115C2×C22⋊C4×C47—24no—
116C2×C22⋊C4×C47—22no—
117C2×C22⋊C4×C47—22no—
118C2×C22⋊C4×C47—22no—
119C2×C22⋊C4×C47—24no—
120C2×C22⋊C4×C47—24no—
121C2×C22⋊C4×C47—42no—
122C2×C22⋊C4×C47—42no—
123C2×C22⋊C4×C47—42no—
124C2×C22⋊C4×C47—42no—
125C2×C22⋊C4×C47D414yes—
126C2×C22⋊C4×C47D418yescomplemented
127#95×C47—24no—
128#95×C47—24no—
129#95×C47—22no—
130#95×C47—22no—
131#95×C47—24no—
132#95×C47—42no—
133C24×C47—22no—
134C24×C47—22no—
135C24×C47—22no—
136C24×C47—22no—
137C24×C47—28no—
138C24×C47—28no—
139C24×C47—216no—
140C24×C47—216no—
141C24×C47—28no—
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—28no—
155C24×C47—28no—
156C24×C47—21no—
157C24×C47—22no—
158C24×C47—21no—
159C24×C47—21no—
160C24×C47—21no—
161C24×C47—21no—
162C24×C47—21no—
163C24×C47—22no—
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—48no—
167C24×C47—48no—
168C24×C47—48no—
169C24×C47—48no—
170C24×C47—48no—
171C24×C47—48no—
172C24×C47—48no—
173C24×C47—48no—
174C24×C47—48no—
175C24×C47—44no—
176C24×C47—44no—
177C24×C47—48no—
178C24×C47—44no—
179C24×C47—44no—
180C24×C47—44no—
181C24×C47—44no—
182C24×C47C2×D412yes—
183C24×C47C2×D414yes—
184C24×C47C2×D414yes—
185C24×C47C2×D412yes—
186C24×C47C2×D412yes—
187C24×C47C2×D412yes—
188C24×C47C2×D412yes—
189C24×C47#4114yes—
190C24×C47#4112yes—
191C24×C47#4112yes—
192C24×C47#4112yes—
193C24×C47C2411yescharacteristic
194C2×D4×C47—216no—
195C2×D4×C47—28no—
196C2×D4×C47—28no—
197C2×D4×C47—28no—
198C2×D4×C47—48no—
199C2×D4×C47—48no—
200C2×D4×C47—48no—
201C2×D4×C47—48no—
202C2×D4×C47—48no—
203C2×D4×C47—48no—
204C2×D4×C47—44no—
205C2×D4×C47—44no—
206C2×D4×C47—44no—
207C2×D4×C47—44no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—22no—
211C22×C4×C47—28no—
212C22×C4×C47—28no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—22no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47—22no—
235C22×C4×C47—28no—
236C22×C4×C47—22no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—22no—
240C22×C4×C47—21no—
241C22×C4×C47—22no—
242C22×C4×C47—22no—
243C22×C4×C47—21no—
244C22×C4×C47—22no—
245C22×C4×C47—21no—
246C22×C4×C47—22no—
247C22×C4×C47—21no—
248C22×C4×C47—22no—
249C22×C4×C47—22no—
250C22×C4×C47—22no—
251C22×C4×C47—22no—
252C22×C4×C47—22no—
253C22×C4×C47—44no—
254C22×C4×C47—48no—
255C22×C4×C47—48no—
256C22×C4×C47—48no—
257C22×C4×C47—48no—
258C22×C4×C47—44no—
259C22×C4×C47—44no—
260C22×C4×C47C2×D412yes—
261C22×C4×C47C2×D414yes—
262C22×C4×C47C2×D412yes—
263C22×C4×C47C2×D414yes—
264C22×C4×C47C2×D412yes—
265C22×C4×C47C2×D414yes—
266C4⋊C4×C47—48no—
267C22⋊C4×C47—216no—
268C22⋊C4×C47—216no—
269C22⋊C4×C47—28no—
270C22⋊C4×C47—216no—
271C22⋊C4×C47—48no—
272C22⋊C4×C47—44no—
273C22⋊C4×C47—48no—
274C22⋊C4×C47—44no—
275C22⋊C4×C47—48no—
276C22⋊C4×C47—44no—
277C22⋊C4×C47—44no—
278C23×C47—22no—
279C23×C47—24no—
280C23×C47—22no—
281C23×C47—24no—
282C23×C47—22no—
283C23×C47—24no—
284C23×C47—22no—
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—232no—
295C23×C47—24no—
296C23×C47—24no—
297C23×C47—24no—
298C23×C47—24no—
299C23×C47—24no—
300C23×C47—24no—
301C23×C47—24no—
302C23×C47—24no—
303C23×C47—24no—
304C23×C47—24no—
305C23×C47—24no—
306C23×C47—24no—
307C23×C47—24no—
308C23×C47—24no—
309C23×C47—24no—
310C23×C47—24no—
311C23×C47—24no—
312C23×C47—24no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—24no—
317C23×C47—24no—
318C23×C47—432no—
319C23×C47—432no—
320C23×C47—416no—
321C23×C47—416no—
322C23×C47—416no—
323C23×C47—416no—
324C23×C47—432no—
325C23×C47—432no—
326C23×C47—416no—
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—416no—
344C23×C47—41no—
345C23×C47—41no—
346C23×C47—41no—
347C23×C47—42no—
348C23×C47—41no—
349C23×C47—42no—
350C23×C47—41no—
351C23×C47—41no—
352C23×C47—41no—
353C23×C47—42no—
354C23×C47—41no—
355C23×C47—42no—
356C23×C47—42no—
357C23×C47—42no—
358C23×C47—42no—
359C23×C47—42no—
360C23×C47—42no—
361C23×C47—42no—
362C23×C47#12014yes—
363C23×C47#12118yes—
364C23×C47#12114yes—
365C23×C47#12114yes—
366C23×C47#12114yes—
367C23×C47#12314yes—
368C23×C47#12314yes—
369C23×C47#12414yes—
370C23×C47C22×D411yescharacteristic
371C23×C47C22×D411yescharacteristic
372C23×C47C22×D411yescharacteristic
373C23×C47C22×D412yes—
374C23×C47C22×D411yescharacteristic
375C23×C47C2×#4111yescharacteristic
376C23×C47C2×#4111yescharacteristic
377C23×C47C2×#4111yescharacteristic
378C23×C47C2×#4112yes—
379C23×C47H(5,𝔽2)12yes—
380C23×C47H(5,𝔽2)12yes—
381D4×C47—432no—
382D4×C47—416no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—24no—
386C2×C4×C47—24no—
387C2×C4×C47—24no—
388C2×C4×C47—22no—
389C2×C4×C47—22no—
390C2×C4×C47—24no—
391C2×C4×C47—22no—
392C2×C4×C47—22no—
393C2×C4×C47—22no—
394C2×C4×C47—22no—
395C2×C4×C47—24no—
396C2×C4×C47—24no—
397C2×C4×C47—24no—
398C2×C4×C47—24no—
399C2×C4×C47—416no—
400C2×C4×C47—416no—
401C2×C4×C47—42no—
402C2×C4×C47—41no—
403C2×C4×C47—41no—
404C2×C4×C47—42no—
405C2×C4×C47—41no—
406C2×C4×C47—41no—
407C2×C4×C47—42no—
408C2×C4×C47—42no—
409C2×C4×C47—42no—
410C2×C4×C47—42no—
411C2×C4×C47—42no—
412C2×C4×C47—42no—
413C2×C4×C47—42no—
414C2×C4×C47—42no—
415C2×C4×C47—41no—
416C2×C4×C47—42no—
417C2×C4×C47—41no—
418C2×C4×C47—42no—
419C2×C4×C47—41no—
420C2×C4×C47—42no—
421C2×C4×C47—41no—
422C2×C4×C47—42no—
423C2×C4×C47—42no—
424C2×C4×C47—41no—
425C2×C4×C47—42no—
426C2×C4×C47—41no—
427C2×C4×C47—42no—
428C2×C4×C47—42no—
429C2×C4×C47—42no—
430C2×C4×C47—42no—
431C2×C4×C47—42no—
432C2×C4×C47#12014yescomplemented
433#14725C4711yesmaximal, characteristic, direct product factor, Sylow
434C22×C47—24no—
435C22×C47—24no—
436C22×C47—24no—
437C22×C47—24no—
438C22×C47—28no—
439C22×C47—24no—
440C22×C47—28no—
441C22×C47—28no—
442C22×C47—28no—
443C22×C47—24no—
444C22×C47—28no—
445C22×C47—28no—
446C22×C47—28no—
447C22×C47—464no—
448C22×C47—44no—
449C22×C47—44no—
450C22×C47—44no—
451C22×C47—44no—
452C22×C47—44no—
453C22×C47—44no—
454C22×C47—44no—
455C22×C47—44no—
456C22×C47—44no—
457C22×C47—44no—
458C22×C47—44no—
459C22×C47—44no—
460C22×C47—42no—
461C22×C47—42no—
462C22×C47—44no—
463C22×C47—44no—
464C22×C47—42no—
465C22×C47—81no—
466C22×C47—81no—
467C22×C47—81no—
468C22×C47—81no—
469C22×C47—82no—
470C22×C47—82no—
471C22×C47#39418yescomplemented
472C22×C47C2×#12011yescharacteristic
473C22×C47C2×#12011yescharacteristic
474C22×C47C2×#12111yescharacteristic
475C22×C47C2×#12112yes—
476C22×C47C2×#12111yescharacteristic
477C22×C47C2×#12111yescharacteristic
478C22×C47C2×#12311yescharacteristic
479C22×C47C2×#12311yescharacteristic
480C22×C47#52511yescharacteristic
481C22×C47#52512yes—
482C22×C47C2×#12411yescharacteristic
483C22×C47#53412yes—
484C22×C47#53411yescharacteristic
485C22×C47#53511yescharacteristic
486C22×C47#53812yes—
487C22×C47D4212yes—
488C22×C47D4212yes—
489C22×C47#54612yes—
490C22×C47#54612yes—
491C22×C47#54612yes—
492C22×C47#54612yes—
493C22×C47#55112yes—
494C22×C47#55112yes—
495C4×C47—24no—
496C4×C47—42no—
497C4×C47—44no—
498C4×C47—42no—
499C4×C47—44no—
500C4×C47—81no—
501C4×C47—81no—
502C4×C47—82no—
503C22×#120C2×C4711yescharacteristic
504C23×C22⋊C4C2×C4711yescharacteristic, complemented
505C2×#394C2×C4712yescomplemented
506C2×#386C2×C4711yescharacteristic, complemented
507C2×#386C2×C4711yescharacteristic, complemented
508C2×#380C2×C4711yescharacteristic, complemented
509C2×#379C2×C4711yescharacteristic, complemented
510#1440C2×C4712yescomplemented
511#1439C2×C4712yescomplemented
512#1438C2×C4712yescomplemented
513C22⋊#95C2×C4711yescharacteristic, complemented
514C2×C47—28no—
515C2×C47—48no—
516C2×C47—82no—
517C2×C47C2×#39411yescharacteristic
518C2×C47#240811yescharacteristic
519C2×C47#241011yescharacteristic
520C2×C47#241012yes—
521C2×C47#241111yescharacteristic
522C2×C47#241212yes—
523C2×C47#241812yes—
524C2×C47#247212yes—
525C2×C47#253411yescharacteristic
526C2×C47#261711yescharacteristic
527C2×C47#284711yescharacteristic
528C26C22×C4711yescharacteristic
529C23×D4C22×C4711yescharacteristic
530C23×D4C22×C4712yes—
531C24×C4C22×C4711yescharacteristic
532C24×C4C22×C4711yescharacteristic
533C2×#120—24no—
534C2×#120—24no—
535C2×#120—24no—
536C22×C4⋊C4C22×C4712yescomplemented
537C22×C22⋊C4—24no—
538C22×C22⋊C4—28no—
539C22×C22⋊C4C22×C4712yes—
540C22×C22⋊C4C22×C4712yes—
541C22×C22⋊C4C22×C4712yes—
542C22×C22⋊C4C22×C4711yescharacteristic
543C22×C22⋊C4C22×C4711yescharacteristic
544C22×C22⋊C4C22×C4711yescharacteristic
545C22×C22⋊C4C22×C4712yes—
546C22×C22⋊C4C22×C4712yes—
547C22×C22⋊C4C22×C4711yescharacteristic, complemented
548C22×C22⋊C4C22×C4712yescomplemented
549C22×C22⋊C4C22×C4711yescharacteristic, complemented
550#394—28no—
551#386—24no—
552#386—24no—
553#380—24no—
554#379—24no—
555C2×#95C22×C4712yescomplemented
556C2×#95C22×C4712yescomplemented
557C2×#95C22×C4711yescharacteristic, complemented
558C2×#95C22×C4712yescomplemented
559C2×#95C22×C4711yescharacteristic, complemented
560C2×#95C22×C4712yescomplemented
561C47#1472511yescharacteristic, direct product factor, Sylow
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C4714yes—
573C25C23×C4711yescharacteristic
574C25C23×C4712yes—
575C25C23×C4711yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C4714yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C4714yescomplemented
600C23×C4C23×C4712yes—
601C23×C4C23×C4711yescharacteristic
602C23×C4C23×C4711yescharacteristic
603C23×C4C23×C4711yescharacteristic
604C23×C4C23×C4712yes—
605C23×C4C23×C4712yes—
606C23×C4C23×C4711yescharacteristic
607C23×C4C23×C4711yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C4714yes—
643C2×C22⋊C4D4×C4718yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C4712yes—
700C24C2×D4×C4714yes—
701C24C2×D4×C4714yes—
702C24C2×D4×C4712yes—
703C24C2×D4×C4712yes—
704C24C2×D4×C4712yes—
705C24C2×D4×C4712yes—
706C24#41×C4714yes—
707C24#41×C4712yes—
708C24#41×C4712yes—
709C24#41×C4712yes—
710C24C24×C4711yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C4712yes—
778C22×C4C2×D4×C4712yes—
779C22×C4C2×D4×C4714yes—
780C22×C4C2×D4×C4714yes—
781C22×C4C2×D4×C4712yes—
782C22×C4C2×D4×C4714yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—432no—
843C23—432no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C4714yes—
880C23#121×C4718yes—
881C23#121×C4714yes—
882C23#121×C4714yes—
883C23#121×C4714yes—
884C23#123×C4714yes—
885C23#123×C4714yes—
886C23#124×C4714yes—
887C23C22×D4×C4711yescharacteristic
888C23C22×D4×C4711yescharacteristic
889C23C22×D4×C4711yescharacteristic
890C23C22×D4×C4712yes—
891C23C22×D4×C4711yescharacteristic
892C23C2×#41×C4711yescharacteristic
893C23C2×#41×C4711yescharacteristic
894C23C2×#41×C4711yescharacteristic
895C23C2×#41×C4712yes—
896C23H(5,𝔽2)×C4712yes—
897C23H(5,𝔽2)×C4712yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C4714yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22C47×#39418yescomplemented
988C22C2×#120×C4711yescharacteristic
989C22C2×#120×C4711yescharacteristic
990C22C2×#121×C4711yescharacteristic
991C22C2×#121×C4711yescharacteristic
992C22C2×#121×C4712yes—
993C22C2×#121×C4711yescharacteristic
994C22C2×#123×C4711yescharacteristic
995C22C2×#123×C4711yescharacteristic
996C22C47×#52511yescharacteristic
997C22C47×#52512yes—
998C22C2×#124×C4711yescharacteristic
999C22C47×#53411yescharacteristic
1000C22C47×#53412yes—
1001C22C47×#53511yescharacteristic
1002C22C47×#53812yes—
1003C22D42×C4712yes—
1004C22D42×C4712yes—
1005C22C47×#54612yes—
1006C22C47×#54612yes—
1007C22C47×#54612yes—
1008C22C47×#54612yes—
1009C22C47×#55112yes—
1010C22C47×#55112yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×C47×#39411yescharacteristic
1023C2C47×#240811yescharacteristic
1024C2C47×#241011yescharacteristic
1025C2C47×#241012yes—
1026C2C47×#241111yescharacteristic
1027C2C47×#241212yes—
1028C2C47×#241812yes—
1029C2C47×#247212yes—
1030C2C47×#253411yescharacteristic
1031C2C47×#261711yescharacteristic
1032C2C47×#284711yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC24C24×C47
prime radicalC22×#120×C47C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C47C2semidirect
3. C2×C47×#394C2semidirect
4. C2×C47×#386C2semidirect
5. C2×C47×#386C2semidirect
6. C2×C47×#380C2semidirect
7. C2×C47×#379C2semidirect
8. C47×#1440C2semidirect
9. C47×#1439C2semidirect
10. C47×#1438C2semidirect
11. C47×C22⋊#95C2semidirect
20. C22×C4⋊C4×C47C22semidirect
31. C22×C22⋊C4×C47C22semidirect
32. C22×C22⋊C4×C47C22semidirect
33. C22×C22⋊C4×C47C22semidirect
39. C2×#95×C47C22semidirect
40. C2×#95×C47C22semidirect
41. C2×#95×C47C22semidirect
42. C2×#95×C47C22semidirect
43. C2×#95×C47C22semidirect
44. C2×#95×C47C22semidirect
82. C23×C4×C47D4semidirect
126. C2×C22⋊C4×C47D4semidirect
432. C2×C4×C47#120semidirect
433. #14725C47direct (N × H)
471. C22×C47#394semidirect
504. C23×C22⋊C4C2×C47semidirect
505. C2×#394C2×C47semidirect
506. C2×#386C2×C47semidirect
507. C2×#386C2×C47semidirect
508. C2×#380C2×C47semidirect
509. C2×#379C2×C47semidirect
510. #1440C2×C47semidirect
511. #1439C2×C47semidirect
512. #1438C2×C47semidirect
513. C22⋊#95C2×C47semidirect
536. C22×C4⋊C4C22×C47semidirect
547. C22×C22⋊C4C22×C47semidirect
548. C22×C22⋊C4C22×C47semidirect
549. C22×C22⋊C4C22×C47semidirect
555. C2×#95C22×C47semidirect
556. C2×#95C22×C47semidirect
557. C2×#95C22×C47semidirect
558. C2×#95C22×C47semidirect
559. C2×#95C22×C47semidirect
560. C2×#95C22×C47semidirect
561. C47#14725direct (N × H)
599. C23×C4D4×C47semidirect
643. C2×C22⋊C4D4×C47semidirect
949. C2×C4#120×C47semidirect
987. C22C47×#394semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C472
C23×C22⋊C4×C472
C2×C47×#3942
C2×C47×#3862
C2×C47×#3802
C2×C47×#3792
C47×#14402
C47×#14392
C47×#14382
C47×C22⋊#952
#1472547