Finite Group Databasebeta

← C2×C47×#2424 #26074348

Subgroups — C2×C47×#2424 #26074348

Order 12032.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C47C211yesmaximal, characteristic, complemented
2C22×#121×C47C211yesmaximal, characteristic, complemented
3C22×#120×C47C211yesmaximal, characteristic, complemented
4C22×#120×C47C211yesmaximal, characteristic, complemented
5C22×C4×D4×C47C211yesmaximal, characteristic, complemented
6C23×C22⋊C4×C47C211yesmaximal, characteristic, complemented
7C47×#2424C2116yesmaximal, direct product factor
8C2×C47×#396C211yesmaximal, characteristic, complemented
9C2×C47×#394C211yesmaximal, characteristic, complemented
10C2×C47×#394C211yesmaximal, characteristic, complemented
11C2×C47×#392C211yesmaximal, characteristic, complemented
12C2×C47×#390C211yesmaximal, characteristic, complemented
13C2×C47×#388C211yesmaximal, characteristic, complemented
14C2×C47×#386C211yesmaximal, characteristic, complemented
15C2×C47×#386C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C26×C47C2211yescharacteristic
18C23×D4×C47C2211yescharacteristic
19C23×D4×C47C2211yescharacteristic
20C23×D4×C47C2211yescharacteristic
21C23×D4×C47C2211yescharacteristic
22C23×D4×C47C2211yescharacteristic
23C23×D4×C47C2211yescharacteristic
24C23×D4×C47C2211yescharacteristic, complemented
25C24×C4×C47C2211yescharacteristic
26C24×C4×C47C2211yescharacteristic
27C24×C4×C47C2211yescharacteristic, complemented
28C2×#121×C47—28no—
29C2×#121×C47—28no—
30C2×#121×C47C2218yescomplemented
31C2×#121×C47C2218yescomplemented
32C2×#120×C47—28no—
33C2×#120×C47—28no—
34C2×#120×C47C2218yescomplemented
35C2×#120×C47C2218yescomplemented
36C2×C4×D4×C47—28no—
37C2×C4×D4×C47C2218yescomplemented
38C22×C4⋊C4×C47C2211yescharacteristic, complemented
39C22×C4⋊C4×C47C2211yescharacteristic, complemented
40C22×C4⋊C4×C47C2211yescharacteristic, complemented
41C22×C4⋊C4×C47C2211yescharacteristic, complemented
42C22×C22⋊C4×C47—28no—
43C22×C22⋊C4×C47C2211yescharacteristic
44C22×C22⋊C4×C47C2211yescharacteristic
45C22×C22⋊C4×C47C2211yescharacteristic
46C22×C22⋊C4×C47C2211yescharacteristic
47C22×C22⋊C4×C47C2211yescharacteristic
48C22×C22⋊C4×C47C2211yescharacteristic
49C22×C22⋊C4×C47C2211yescharacteristic
50C22×C22⋊C4×C47C2211yescharacteristic
51C22×C22⋊C4×C47C2211yescharacteristic
52C22×C22⋊C4×C47C2211yescharacteristic
53C22×C22⋊C4×C47C2218yescomplemented
54C22×C22⋊C4×C47C2211yescharacteristic, complemented
55C22×C22⋊C4×C47C2211yescharacteristic, complemented
56C22×C22⋊C4×C47C2211yescharacteristic, complemented
57C22×C22⋊C4×C47C2211yescharacteristic, complemented
58C22×C22⋊C4×C47C2211yescharacteristic, complemented
59C22×C42×C47C2211yescharacteristic, complemented
60C47×#396C2218yescomplemented
61C47×#394C2218yescomplemented
62C47×#394C2218yescomplemented
63C47×#392C2218yescomplemented
64C47×#390C2218yescomplemented
65C47×#388C2218yescomplemented
66C47×#386C2218yescomplemented
67C47×#386C2218yescomplemented
68C47×#385C2218yescomplemented
69C2×#95×C47C2211yescharacteristic, complemented
70C2×#95×C47C2211yescharacteristic, complemented
71C2×#95×C47C2211yescharacteristic, complemented
72C2×#95×C47C2211yescharacteristic, complemented
73C25×C47—24no—
74C25×C47—24no—
75C25×C47—24no—
76C25×C47—24no—
77C25×C47—24no—
78C25×C47—42no—
79C25×C47—42no—
80C25×C47C2311yescharacteristic
81C25×C47C2311yescharacteristic
82C25×C47C2311yescharacteristic
83C25×C47C2311yescharacteristic
84C25×C47C2314yes—
85C25×C47C2311yescharacteristic
86C22×D4×C47—24no—
87C22×D4×C47—24no—
88C22×D4×C47—24no—
89C22×D4×C47—24no—
90C22×D4×C47—24no—
91C22×D4×C47—24no—
92C22×D4×C47—24no—
93C22×D4×C47—24no—
94C22×D4×C47—24no—
95C22×D4×C47—24no—
96C22×D4×C47—24no—
97C22×D4×C47—24no—
98C22×D4×C47—24no—
99C22×D4×C47—24no—
100C22×D4×C47—24no—
101C22×D4×C47—42no—
102C22×D4×C47—42no—
103C22×D4×C47—42no—
104C22×D4×C47—42no—
105C22×D4×C47—42no—
106C22×D4×C47D418yescomplemented
107C22×D4×C47C2314yes—
108C22×D4×C47C2314yes—
109C22×D4×C47C2314yes—
110C22×D4×C47C2314yes—
111C22×D4×C47C2314yes—
112C22×D4×C47C2314yes—
113C22×D4×C47C2314yescomplemented
114C23×C4×C47—24no—
115C23×C4×C47—24no—
116C23×C4×C47—24no—
117C23×C4×C47—24no—
118C23×C4×C47—24no—
119C23×C4×C47—24no—
120C23×C4×C47—42no—
121C23×C4×C47—42no—
122C23×C4×C47—42no—
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2314yes—
129C23×C4×C47C2314yes—
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2314yescomplemented
136#121×C47—232no—
137#121×C47—232no—
138#120×C47—232no—
139#120×C47—232no—
140C4×D4×C47—232no—
141C2×C4⋊C4×C47—24no—
142C2×C4⋊C4×C47—24no—
143C2×C4⋊C4×C47—24no—
144C2×C4⋊C4×C47—42no—
145C2×C4⋊C4×C47C2314yescomplemented
146C2×C4⋊C4×C47C2314yescomplemented
147C2×C4⋊C4×C47C2314yescomplemented
148C2×C4⋊C4×C47C2314yescomplemented
149C2×C22⋊C4×C47—24no—
150C2×C22⋊C4×C47—24no—
151C2×C22⋊C4×C47—24no—
152C2×C22⋊C4×C47—24no—
153C2×C22⋊C4×C47—24no—
154C2×C22⋊C4×C47—24no—
155C2×C22⋊C4×C47—24no—
156C2×C22⋊C4×C47—24no—
157C2×C22⋊C4×C47—24no—
158C2×C22⋊C4×C47—24no—
159C2×C22⋊C4×C47—24no—
160C2×C22⋊C4×C47—24no—
161C2×C22⋊C4×C47—232no—
162C2×C22⋊C4×C47—42no—
163C2×C22⋊C4×C47D418yescomplemented
164C2×C22⋊C4×C47D418yescomplemented
165C2×C22⋊C4×C47C2314yes—
166C2×C22⋊C4×C47C2314yes—
167C2×C22⋊C4×C47C2314yes—
168C2×C22⋊C4×C47C2314yes—
169C2×C22⋊C4×C47C2314yes—
170C2×C22⋊C4×C47C2314yes—
171C2×C22⋊C4×C47C2314yes—
172C2×C22⋊C4×C47C2314yes—
173C2×C22⋊C4×C47C2314yes—
174C2×C22⋊C4×C47C2314yes—
175C2×C22⋊C4×C47C2314yescomplemented
176C2×C22⋊C4×C47C2314yescomplemented
177C2×C22⋊C4×C47C2314yescomplemented
178C2×C22⋊C4×C47C2314yescomplemented
179C2×C22⋊C4×C47C2314yescomplemented
180C2×C42×C47—24no—
181C2×C42×C47C2314yescomplemented
182#95×C47C2314yescomplemented
183#95×C47C2314yescomplemented
184#95×C47C2314yescomplemented
185#95×C47C2314yescomplemented
186C24×C47—22no—
187C24×C47—22no—
188C24×C47—22no—
189C24×C47—22no—
190C24×C47—232no—
191C24×C47—28no—
192C24×C47—22no—
193C24×C47—22no—
194C24×C47—22no—
195C24×C47—22no—
196C24×C47—22no—
197C24×C47—22no—
198C24×C47—22no—
199C24×C47—22no—
200C24×C47—22no—
201C24×C47—28no—
202C24×C47—28no—
203C24×C47—22no—
204C24×C47—22no—
205C24×C47—22no—
206C24×C47—22no—
207C24×C47—22no—
208C24×C47—22no—
209C24×C47—22no—
210C24×C47—22no—
211C24×C47—22no—
212C24×C47—22no—
213C24×C47—22no—
214C24×C47—28no—
215C24×C47—28no—
216C24×C47—22no—
217C24×C47—22no—
218C24×C47—22no—
219C24×C47—22no—
220C24×C47—22no—
221C24×C47—44no—
222C24×C47—44no—
223C24×C47—416no—
224C24×C47—416no—
225C24×C47—416no—
226C24×C47—416no—
227C24×C47—416no—
228C24×C47—416no—
229C24×C47C2×D414yes—
230C24×C47C2×D414yes—
231C24×C47C2×D414yes—
232C24×C47C2×D414yes—
233C24×C47#4114yes—
234C24×C47#4114yes—
235C24×C47C2412yes—
236C24×C47C2412yes—
237C24×C47C2412yes—
238C24×C47C2412yes—
239C24×C47C2412yes—
240C24×C47C2411yescharacteristic
241C2×D4×C47—232no—
242C2×D4×C47—28no—
243C2×D4×C47—28no—
244C2×D4×C47—28no—
245C2×D4×C47—28no—
246C2×D4×C47—28no—
247C2×D4×C47—28no—
248C2×D4×C47—28no—
249C2×D4×C47—28no—
250C2×D4×C47—28no—
251C2×D4×C47—28no—
252C2×D4×C47—28no—
253C2×D4×C47—28no—
254C2×D4×C47—28no—
255C2×D4×C47—28no—
256C2×D4×C47—28no—
257C2×D4×C47—44no—
258C2×D4×C47—44no—
259C2×D4×C47—44no—
260C2×D4×C47—44no—
261C2×D4×C47—44no—
262C2×D4×C47—416no—
263C2×D4×C47—416no—
264C2×D4×C47—416no—
265C2×D4×C47—416no—
266C2×D4×C47—416no—
267C2×D4×C47—416no—
268C2×D4×C47C2×D4116yescomplemented
269C22×C4×C47—22no—
270C22×C4×C47—22no—
271C22×C4×C47—22no—
272C22×C4×C47—22no—
273C22×C4×C47—22no—
274C22×C4×C47—22no—
275C22×C4×C47—22no—
276C22×C4×C47—22no—
277C22×C4×C47—22no—
278C22×C4×C47—22no—
279C22×C4×C47—22no—
280C22×C4×C47—22no—
281C22×C4×C47—22no—
282C22×C4×C47—22no—
283C22×C4×C47—22no—
284C22×C4×C47—22no—
285C22×C4×C47—22no—
286C22×C4×C47—22no—
287C22×C4×C47—22no—
288C22×C4×C47—28no—
289C22×C4×C47—28no—
290C22×C4×C47—22no—
291C22×C4×C47—22no—
292C22×C4×C47—22no—
293C22×C4×C47—22no—
294C22×C4×C47—22no—
295C22×C4×C47—22no—
296C22×C4×C47—28no—
297C22×C4×C47—28no—
298C22×C4×C47—28no—
299C22×C4×C47—28no—
300C22×C4×C47—44no—
301C22×C4×C47—44no—
302C22×C4×C47—44no—
303C22×C4×C47—416no—
304C22×C4×C47—416no—
305C22×C4×C47—416no—
306C22×C4×C47C2×D414yes—
307C22×C4×C47C2×D414yes—
308C22×C4×C47C2×D414yes—
309C22×C4×C47C2×D414yes—
310C22×C4×C47C2×D414yes—
311C22×C4×C47C2412yes—
312C22×C4×C47C2412yes—
313C22×C4×C47C2412yes—
314C22×C4×C47C2412yes—
315C22×C4×C47C2412yes—
316C22×C4×C47C2412yes—
317C22×C4×C47C2412yes—
318C22×C4×C47C2412yes—
319C22×C4×C47C2412yes—
320C22×C4×C47C2412yes—
321C4⋊C4×C47—28no—
322C4⋊C4×C47—28no—
323C4⋊C4×C47—28no—
324C4⋊C4×C47—44no—
325C22⋊C4×C47—28no—
326C22⋊C4×C47—28no—
327C22⋊C4×C47—28no—
328C22⋊C4×C47—28no—
329C22⋊C4×C47—28no—
330C22⋊C4×C47—28no—
331C22⋊C4×C47—28no—
332C22⋊C4×C47—28no—
333C22⋊C4×C47—28no—
334C22⋊C4×C47—28no—
335C22⋊C4×C47—28no—
336C22⋊C4×C47—28no—
337C22⋊C4×C47—44no—
338C22⋊C4×C47C2×D4116yescomplemented
339C22⋊C4×C47C2×D4116yescomplemented
340C42×C47—28no—
341C23×C47—28no—
342C23×C47—28no—
343C23×C47—28no—
344C23×C47—28no—
345C23×C47—28no—
346C23×C47—28no—
347C23×C47—22no—
348C23×C47—22no—
349C23×C47—22no—
350C23×C47—22no—
351C23×C47—232no—
352C23×C47—28no—
353C23×C47—28no—
354C23×C47—28no—
355C23×C47—28no—
356C23×C47—28no—
357C23×C47—28no—
358C23×C47—28no—
359C23×C47—28no—
360C23×C47—28no—
361C23×C47—22no—
362C23×C47—22no—
363C23×C47—22no—
364C23×C47—22no—
365C23×C47—22no—
366C23×C47—22no—
367C23×C47—22no—
368C23×C47—22no—
369C23×C47—22no—
370C23×C47—22no—
371C23×C47—22no—
372C23×C47—22no—
373C23×C47—22no—
374C23×C47—22no—
375C23×C47—22no—
376C23×C47—22no—
377C23×C47—22no—
378C23×C47—22no—
379C23×C47—22no—
380C23×C47—22no—
381C23×C47—22no—
382C23×C47—22no—
383C23×C47—22no—
384C23×C47—22no—
385C23×C47—22no—
386C23×C47—416no—
387C23×C47—416no—
388C23×C47—416no—
389C23×C47—416no—
390C23×C47—4128no—
391C23×C47—416no—
392C23×C47—44no—
393C23×C47—44no—
394C23×C47—416no—
395C23×C47—44no—
396C23×C47—44no—
397C23×C47—44no—
398C23×C47—44no—
399C23×C47—44no—
400C23×C47—44no—
401C23×C47—44no—
402C23×C47—44no—
403C23×C47—44no—
404C23×C47—44no—
405C23×C47—44no—
406C23×C47—44no—
407C23×C47—44no—
408C23×C47—44no—
409C23×C47—44no—
410C23×C47—44no—
411C23×C47—44no—
412C23×C47#121116yescomplemented
413C23×C47C22×D414yes—
414C23×C47C22×D414yes—
415C23×C47C22×D414yes—
416C23×C47C22×D414yes—
417C23×C47C22×D412yes—
418C23×C47C22×D412yes—
419C23×C47C22×D412yes—
420C23×C47C2×#4114yes—
421C23×C47C2×#4114yes—
422C23×C47C2×#4112yes—
423C23×C47C2×#4112yes—
424C23×C47H(5,𝔽2)12yes—
425C23×C47H(5,𝔽2)12yes—
426C23×C47C2511yescharacteristic
427D4×C47—232no—
428D4×C47—416no—
429D4×C47—416no—
430D4×C47—416no—
431D4×C47—416no—
432D4×C47—416no—
433D4×C47—416no—
434C2×C4×C47—28no—
435C2×C4×C47—28no—
436C2×C4×C47—28no—
437C2×C4×C47—28no—
438C2×C4×C47—28no—
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—22no—
442C2×C4×C47—22no—
443C2×C4×C47—22no—
444C2×C4×C47—22no—
445C2×C4×C47—22no—
446C2×C4×C47—22no—
447C2×C4×C47—22no—
448C2×C4×C47—22no—
449C2×C4×C47—22no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—22no—
453C2×C4×C47—22no—
454C2×C4×C47—22no—
455C2×C4×C47—22no—
456C2×C4×C47—22no—
457C2×C4×C47—22no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—416no—
465C2×C4×C47—416no—
466C2×C4×C47—416no—
467C2×C4×C47—44no—
468C2×C4×C47—44no—
469C2×C4×C47—44no—
470C2×C4×C47—44no—
471C2×C4×C47—44no—
472C2×C4×C47C22×D414yes—
473C2×C4×C47C22×D414yes—
474C2×C4×C47C22×D414yes—
475C2×C4×C47C22×D414yes—
476C2×C4×C47C22×D414yes—
477C2×#2424C4711yesmaximal, characteristic, direct product factor, Sylow
478C22×C47—24no—
479C22×C47—232no—
480C22×C47—24no—
481C22×C47—24no—
482C22×C47—24no—
483C22×C47—24no—
484C22×C47—24no—
485C22×C47—24no—
486C22×C47—24no—
487C22×C47—24no—
488C22×C47—24no—
489C22×C47—24no—
490C22×C47—24no—
491C22×C47—24no—
492C22×C47—24no—
493C22×C47—24no—
494C22×C47—464no—
495C22×C47—42no—
496C22×C47—42no—
497C22×C47—42no—
498C22×C47—416no—
499C22×C47—416no—
500C22×C47—416no—
501C22×C47—42no—
502C22×C47—42no—
503C22×C47—42no—
504C22×C47—42no—
505C22×C47—42no—
506C22×C47—42no—
507C22×C47—42no—
508C22×C47—42no—
509C22×C47—42no—
510C22×C47—42no—
511C22×C47—42no—
512C22×C47—42no—
513C22×C47—42no—
514C22×C47—42no—
515C22×C47—42no—
516C22×C47—42no—
517C22×C47—88no—
518C22×C47C2×#12114yes—
519C22×C47C2×#12118yescomplemented
520C22×C47#52514yes—
521C22×C47#53814yes—
522C22×C47D4214yes—
523C22×C47D4214yes—
524C22×C47#54614yes—
525C22×C47#54614yes—
526C22×C47C23×D411yescharacteristic
527C22×C47C23×D411yescharacteristic
528C22×C47C23×D411yescharacteristic
529C22×C47C22×#4111yescharacteristic
530C22×C47C22×#4111yescharacteristic
531C22×C47C2×H(5,𝔽2)11yescharacteristic
532C22×C47C2×H(5,𝔽2)11yescharacteristic
533C4×C47—24no—
534C4×C47—24no—
535C4×C47—24no—
536C4×C47—24no—
537C4×C47—24no—
538C4×C47—42no—
539C4×C47—42no—
540C4×C47—42no—
541C4×C47—42no—
542C4×C47—42no—
543C22×#121C2×C4711yescharacteristic, complemented
544C22×#121C2×C4711yescharacteristic, complemented
545C22×#120C2×C4711yescharacteristic, complemented
546C22×#120C2×C4711yescharacteristic, complemented
547C22×C4×D4C2×C4711yescharacteristic, complemented
548C23×C22⋊C4C2×C4711yescharacteristic, complemented
549#2424C2×C47116yesdirect product factor
550C2×#396C2×C4711yescharacteristic, complemented
551C2×#394C2×C4711yescharacteristic, complemented
552C2×#394C2×C4711yescharacteristic, complemented
553C2×#392C2×C4711yescharacteristic, complemented
554C2×#390C2×C4711yescharacteristic, complemented
555C2×#388C2×C4711yescharacteristic, complemented
556C2×#386C2×C4711yescharacteristic, complemented
557C2×#386C2×C4711yescharacteristic, complemented
558C2×#385C2×C4711yescharacteristic, complemented
559C2×C47—28no—
560C2×C47—44no—
561C2×C47—44no—
562C2×C47—44no—
563C2×C47—82no—
564C2×C47#242418yesdirect product factor
565C2×C47C22×#12111yescharacteristic
566C2×C47C2×#52511yescharacteristic
567C2×C47C2×#53811yescharacteristic
568C2×C47C2×D4211yescharacteristic
569C2×C47C2×D4211yescharacteristic
570C2×C47C2×#54611yescharacteristic
571C2×C47C2×#54611yescharacteristic
572C26C22×C4711yescharacteristic
573C23×D4C22×C4711yescharacteristic
574C23×D4C22×C4711yescharacteristic
575C23×D4C22×C4711yescharacteristic
576C23×D4C22×C4711yescharacteristic
577C23×D4C22×C4711yescharacteristic
578C23×D4C22×C4711yescharacteristic
579C23×D4C22×C4711yescharacteristic, complemented
580C24×C4C22×C4711yescharacteristic
581C24×C4C22×C4711yescharacteristic
582C24×C4C22×C4711yescharacteristic, complemented
583C2×#121—28no—
584C2×#121—28no—
585C2×#121C22×C4718yescomplemented
586C2×#121C22×C4718yescomplemented
587C2×#120—28no—
588C2×#120—28no—
589C2×#120C22×C4718yescomplemented
590C2×#120C22×C4718yescomplemented
591C2×C4×D4—28no—
592C2×C4×D4C22×C4718yescomplemented
593C22×C4⋊C4C22×C4711yescharacteristic, complemented
594C22×C4⋊C4C22×C4711yescharacteristic, complemented
595C22×C4⋊C4C22×C4711yescharacteristic, complemented
596C22×C4⋊C4C22×C4711yescharacteristic, complemented
597C22×C22⋊C4—28no—
598C22×C22⋊C4C22×C4711yescharacteristic
599C22×C22⋊C4C22×C4711yescharacteristic
600C22×C22⋊C4C22×C4711yescharacteristic
601C22×C22⋊C4C22×C4711yescharacteristic
602C22×C22⋊C4C22×C4711yescharacteristic
603C22×C22⋊C4C22×C4711yescharacteristic
604C22×C22⋊C4C22×C4711yescharacteristic
605C22×C22⋊C4C22×C4711yescharacteristic
606C22×C22⋊C4C22×C4711yescharacteristic
607C22×C22⋊C4C22×C4711yescharacteristic
608C22×C22⋊C4C22×C4718yescomplemented
609C22×C22⋊C4C22×C4711yescharacteristic, complemented
610C22×C22⋊C4C22×C4711yescharacteristic, complemented
611C22×C22⋊C4C22×C4711yescharacteristic, complemented
612C22×C22⋊C4C22×C4711yescharacteristic, complemented
613C22×C22⋊C4C22×C4711yescharacteristic, complemented
614C22×C42C22×C4711yescharacteristic, complemented
615#396C22×C4718yescomplemented
616#394C22×C4718yescomplemented
617#394C22×C4718yescomplemented
618#392C22×C4718yescomplemented
619#390C22×C4718yescomplemented
620#388C22×C4718yescomplemented
621#386C22×C4718yescomplemented
622#386C22×C4718yescomplemented
623#385C22×C4718yescomplemented
624C2×#95C22×C4711yescharacteristic, complemented
625C2×#95C22×C4711yescharacteristic, complemented
626C2×#95C22×C4711yescharacteristic, complemented
627C2×#95C22×C4711yescharacteristic, complemented
628C47C2×#242411yescharacteristic, direct product factor, Sylow
629C25—24no—
630C25—24no—
631C25—24no—
632C25—24no—
633C25—24no—
634C25—42no—
635C25—42no—
636C25C23×C4711yescharacteristic
637C25C23×C4711yescharacteristic
638C25C23×C4711yescharacteristic
639C25C23×C4711yescharacteristic
640C25C23×C4714yes—
641C25C23×C4711yescharacteristic
642C22×D4—24no—
643C22×D4—24no—
644C22×D4—24no—
645C22×D4—24no—
646C22×D4—24no—
647C22×D4—24no—
648C22×D4—24no—
649C22×D4—24no—
650C22×D4—24no—
651C22×D4—24no—
652C22×D4—24no—
653C22×D4—24no—
654C22×D4—24no—
655C22×D4—24no—
656C22×D4—24no—
657C22×D4—42no—
658C22×D4—42no—
659C22×D4—42no—
660C22×D4—42no—
661C22×D4—42no—
662C22×D4D4×C4718yescomplemented
663C22×D4C23×C4714yes—
664C22×D4C23×C4714yes—
665C22×D4C23×C4714yes—
666C22×D4C23×C4714yes—
667C22×D4C23×C4714yes—
668C22×D4C23×C4714yes—
669C22×D4C23×C4714yescomplemented
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—24no—
673C23×C4—24no—
674C23×C4—24no—
675C23×C4—24no—
676C23×C4—42no—
677C23×C4—42no—
678C23×C4—42no—
679C23×C4C23×C4711yescharacteristic
680C23×C4C23×C4711yescharacteristic
681C23×C4C23×C4711yescharacteristic
682C23×C4C23×C4711yescharacteristic
683C23×C4C23×C4711yescharacteristic
684C23×C4C23×C4714yes—
685C23×C4C23×C4714yes—
686C23×C4C23×C4711yescharacteristic
687C23×C4C23×C4711yescharacteristic
688C23×C4C23×C4711yescharacteristic
689C23×C4C23×C4711yescharacteristic
690C23×C4C23×C4711yescharacteristic
691C23×C4C23×C4714yescomplemented
692#121—232no—
693#121—232no—
694#120—232no—
695#120—232no—
696C4×D4—232no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—24no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—42no—
701C2×C4⋊C4C23×C4714yescomplemented
702C2×C4⋊C4C23×C4714yescomplemented
703C2×C4⋊C4C23×C4714yescomplemented
704C2×C4⋊C4C23×C4714yescomplemented
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—232no—
718C2×C22⋊C4—42no—
719C2×C22⋊C4D4×C4718yescomplemented
720C2×C22⋊C4D4×C4718yescomplemented
721C2×C22⋊C4C23×C4714yes—
722C2×C22⋊C4C23×C4714yes—
723C2×C22⋊C4C23×C4714yes—
724C2×C22⋊C4C23×C4714yes—
725C2×C22⋊C4C23×C4714yes—
726C2×C22⋊C4C23×C4714yes—
727C2×C22⋊C4C23×C4714yes—
728C2×C22⋊C4C23×C4714yes—
729C2×C22⋊C4C23×C4714yes—
730C2×C22⋊C4C23×C4714yes—
731C2×C22⋊C4C23×C4714yescomplemented
732C2×C22⋊C4C23×C4714yescomplemented
733C2×C22⋊C4C23×C4714yescomplemented
734C2×C22⋊C4C23×C4714yescomplemented
735C2×C22⋊C4C23×C4714yescomplemented
736C2×C42—24no—
737C2×C42C23×C4714yescomplemented
738#95C23×C4714yescomplemented
739#95C23×C4714yescomplemented
740#95C23×C4714yescomplemented
741#95C23×C4714yescomplemented
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—232no—
747C24—28no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—28no—
758C24—28no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—22no—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—22no—
769C24—22no—
770C24—28no—
771C24—28no—
772C24—22no—
773C24—22no—
774C24—22no—
775C24—22no—
776C24—22no—
777C24—44no—
778C24—44no—
779C24—416no—
780C24—416no—
781C24—416no—
782C24—416no—
783C24—416no—
784C24—416no—
785C24C2×D4×C4714yes—
786C24C2×D4×C4714yes—
787C24C2×D4×C4714yes—
788C24C2×D4×C4714yes—
789C24#41×C4714yes—
790C24#41×C4714yes—
791C24C24×C4712yes—
792C24C24×C4712yes—
793C24C24×C4712yes—
794C24C24×C4712yes—
795C24C24×C4712yes—
796C24C24×C4711yescharacteristic
797C2×D4—232no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—416no—
819C2×D4—416no—
820C2×D4—416no—
821C2×D4—416no—
822C2×D4—416no—
823C2×D4—416no—
824C2×D4C2×D4×C47116yescomplemented
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—416no—
860C22×C4—416no—
861C22×C4—416no—
862C22×C4C2×D4×C4714yes—
863C22×C4C2×D4×C4714yes—
864C22×C4C2×D4×C4714yes—
865C22×C4C2×D4×C4714yes—
866C22×C4C2×D4×C4714yes—
867C22×C4C24×C4712yes—
868C22×C4C24×C4712yes—
869C22×C4C24×C4712yes—
870C22×C4C24×C4712yes—
871C22×C4C24×C4712yes—
872C22×C4C24×C4712yes—
873C22×C4C24×C4712yes—
874C22×C4C24×C4712yes—
875C22×C4C24×C4712yes—
876C22×C4C24×C4712yes—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—44no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—44no—
894C22⋊C4C2×D4×C47116yescomplemented
895C22⋊C4C2×D4×C47116yescomplemented
896C42—28no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—232no—
908C23—28no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—28no—
915C23—28no—
916C23—28no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—416no—
943C23—416no—
944C23—416no—
945C23—416no—
946C23—4128no—
947C23—416no—
948C23—44no—
949C23—44no—
950C23—416no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—44no—
955C23—44no—
956C23—44no—
957C23—44no—
958C23—44no—
959C23—44no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—44no—
968C23#121×C47116yescomplemented
969C23C22×D4×C4714yes—
970C23C22×D4×C4714yes—
971C23C22×D4×C4714yes—
972C23C22×D4×C4714yes—
973C23C22×D4×C4712yes—
974C23C22×D4×C4712yes—
975C23C22×D4×C4712yes—
976C23C2×#41×C4714yes—
977C23C2×#41×C4714yes—
978C23C2×#41×C4712yes—
979C23C2×#41×C4712yes—
980C23H(5,𝔽2)×C4712yes—
981C23H(5,𝔽2)×C4712yes—
982C23C25×C4711yescharacteristic
983D4—232no—
984D4—416no—
985D4—416no—
986D4—416no—
987D4—416no—
988D4—416no—
989D4—416no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—416no—
1021C2×C4—416no—
1022C2×C4—416no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4C22×D4×C4714yes—
1029C2×C4C22×D4×C4714yes—
1030C2×C4C22×D4×C4714yes—
1031C2×C4C22×D4×C4714yes—
1032C2×C4C22×D4×C4714yes—
1033C22—24no—
1034C22—232no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—464no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—416no—
1054C22—416no—
1055C22—416no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—88no—
1073C22C2×#121×C4714yes—
1074C22C2×#121×C4718yescomplemented
1075C22C47×#52514yes—
1076C22C47×#53814yes—
1077C22D42×C4714yes—
1078C22D42×C4714yes—
1079C22C47×#54614yes—
1080C22C47×#54614yes—
1081C22C23×D4×C4711yescharacteristic
1082C22C23×D4×C4711yescharacteristic
1083C22C23×D4×C4711yescharacteristic
1084C22C22×#41×C4711yescharacteristic
1085C22C22×#41×C4711yescharacteristic
1086C22C2×H(5,𝔽2)×C4711yescharacteristic
1087C22C2×H(5,𝔽2)×C4711yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—24no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C2—28no—
1099C2—44no—
1100C2—44no—
1101C2—44no—
1102C2—82no—
1103C2C47×#242418yesdirect product factor
1104C2C22×#121×C4711yescharacteristic
1105C2C2×C47×#52511yescharacteristic
1106C2C2×C47×#53811yescharacteristic
1107C2C2×D42×C4711yescharacteristic
1108C2C2×D42×C4711yescharacteristic
1109C2C2×C47×#54611yescharacteristic
1110C2C2×C47×#54611yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC23C25×C47
LCSG ▷ C23 ▷ 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×#121×C47C2semidirect
3. C22×#120×C47C2semidirect
4. C22×#120×C47C2semidirect
5. C22×C4×D4×C47C2semidirect
6. C23×C22⋊C4×C47C2semidirect
7. C47×#2424C2direct (N × H)
8. C2×C47×#396C2semidirect
9. C2×C47×#394C2semidirect
10. C2×C47×#394C2semidirect
11. C2×C47×#392C2semidirect
12. C2×C47×#390C2semidirect
13. C2×C47×#388C2semidirect
14. C2×C47×#386C2semidirect
15. C2×C47×#386C2semidirect
16. C2×C47×#385C2semidirect
24. C23×D4×C47C22semidirect
27. C24×C4×C47C22semidirect
30. C2×#121×C47C22semidirect
31. C2×#121×C47C22semidirect
34. C2×#120×C47C22semidirect
35. C2×#120×C47C22semidirect
37. C2×C4×D4×C47C22semidirect
38. C22×C4⋊C4×C47C22semidirect
39. C22×C4⋊C4×C47C22semidirect
40. C22×C4⋊C4×C47C22semidirect
41. C22×C4⋊C4×C47C22semidirect
53. C22×C22⋊C4×C47C22semidirect
54. C22×C22⋊C4×C47C22semidirect
55. C22×C22⋊C4×C47C22semidirect
56. C22×C22⋊C4×C47C22semidirect
57. C22×C22⋊C4×C47C22semidirect
58. C22×C22⋊C4×C47C22semidirect
59. C22×C42×C47C22semidirect
60. C47×#396C22semidirect
61. C47×#394C22semidirect
62. C47×#394C22semidirect
63. C47×#392C22semidirect
64. C47×#390C22semidirect
65. C47×#388C22semidirect
66. C47×#386C22semidirect
67. C47×#386C22semidirect
68. C47×#385C22semidirect
69. C2×#95×C47C22semidirect
70. C2×#95×C47C22semidirect
71. C2×#95×C47C22semidirect
72. C2×#95×C47C22semidirect
106. C22×D4×C47D4semidirect
113. C22×D4×C47C23semidirect
135. C23×C4×C47C23semidirect
145. C2×C4⋊C4×C47C23semidirect
146. C2×C4⋊C4×C47C23semidirect
147. C2×C4⋊C4×C47C23semidirect
148. C2×C4⋊C4×C47C23semidirect
163. C2×C22⋊C4×C47D4semidirect
164. C2×C22⋊C4×C47D4semidirect
175. C2×C22⋊C4×C47C23semidirect
176. C2×C22⋊C4×C47C23semidirect
177. C2×C22⋊C4×C47C23semidirect
178. C2×C22⋊C4×C47C23semidirect
179. C2×C22⋊C4×C47C23semidirect
181. C2×C42×C47C23semidirect
182. #95×C47C23semidirect
183. #95×C47C23semidirect
184. #95×C47C23semidirect
185. #95×C47C23semidirect
268. C2×D4×C47C2×D4semidirect
338. C22⋊C4×C47C2×D4semidirect
339. C22⋊C4×C47C2×D4semidirect
412. C23×C47#121semidirect
477. C2×#2424C47direct (N × H)
519. C22×C47C2×#121semidirect
543. C22×#121C2×C47semidirect
544. C22×#121C2×C47semidirect
545. C22×#120C2×C47semidirect
546. C22×#120C2×C47semidirect
547. C22×C4×D4C2×C47semidirect
548. C23×C22⋊C4C2×C47semidirect
549. #2424C2×C47direct (N × H)
550. C2×#396C2×C47semidirect
551. C2×#394C2×C47semidirect
552. C2×#394C2×C47semidirect
553. C2×#392C2×C47semidirect
554. C2×#390C2×C47semidirect
555. C2×#388C2×C47semidirect
556. C2×#386C2×C47semidirect
557. C2×#386C2×C47semidirect
558. C2×#385C2×C47semidirect
564. C2×C47#2424direct (N × H)
579. C23×D4C22×C47semidirect
582. C24×C4C22×C47semidirect
585. C2×#121C22×C47semidirect
586. C2×#121C22×C47semidirect
589. C2×#120C22×C47semidirect
590. C2×#120C22×C47semidirect
592. C2×C4×D4C22×C47semidirect
593. C22×C4⋊C4C22×C47semidirect
594. C22×C4⋊C4C22×C47semidirect
595. C22×C4⋊C4C22×C47semidirect
596. C22×C4⋊C4C22×C47semidirect
608. C22×C22⋊C4C22×C47semidirect
609. C22×C22⋊C4C22×C47semidirect
610. C22×C22⋊C4C22×C47semidirect
611. C22×C22⋊C4C22×C47semidirect
612. C22×C22⋊C4C22×C47semidirect
613. C22×C22⋊C4C22×C47semidirect
614. C22×C42C22×C47semidirect
615. #396C22×C47semidirect
616. #394C22×C47semidirect
617. #394C22×C47semidirect
618. #392C22×C47semidirect
619. #390C22×C47semidirect
620. #388C22×C47semidirect
621. #386C22×C47semidirect
622. #386C22×C47semidirect
623. #385C22×C47semidirect
624. C2×#95C22×C47semidirect
625. C2×#95C22×C47semidirect
626. C2×#95C22×C47semidirect
627. C2×#95C22×C47semidirect
628. C47C2×#2424direct (N × H)
662. C22×D4D4×C47semidirect
669. C22×D4C23×C47semidirect
691. C23×C4C23×C47semidirect
701. C2×C4⋊C4C23×C47semidirect
702. C2×C4⋊C4C23×C47semidirect
703. C2×C4⋊C4C23×C47semidirect
704. C2×C4⋊C4C23×C47semidirect
719. C2×C22⋊C4D4×C47semidirect
720. C2×C22⋊C4D4×C47semidirect
731. C2×C22⋊C4C23×C47semidirect
732. C2×C22⋊C4C23×C47semidirect
733. C2×C22⋊C4C23×C47semidirect
734. C2×C22⋊C4C23×C47semidirect
735. C2×C22⋊C4C23×C47semidirect
737. C2×C42C23×C47semidirect
738. #95C23×C47semidirect
739. #95C23×C47semidirect
740. #95C23×C47semidirect
741. #95C23×C47semidirect
824. C2×D4C2×D4×C47semidirect
894. C22⋊C4C2×D4×C47semidirect
895. C22⋊C4C2×D4×C47semidirect
968. C23#121×C47semidirect
1074. C22C2×#121×C47semidirect
1103. C2C47×#2424direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#121×C472
C22×#120×C472
C22×C4×D4×C472
C23×C22⋊C4×C472
C47×#24242
C2×C47×#3962
C2×C47×#3942
C2×C47×#3922
C2×C47×#3902
C2×C47×#3882
C2×C47×#3862
C2×C47×#3852
C2×#242447