Finite Group Databasebeta

← C47×#16270 #26055968

Subgroups — C47×#16270 #26055968

Order 12032.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#397C211yesmaximal, characteristic, complemented
2C2×C47×#392C211yesmaximal, characteristic
3C2×C47×#386C211yesmaximal, characteristic, complemented
4C2×C47×#386C211yesmaximal, characteristic, complemented
5C47×#1443C211yesmaximal, characteristic, complemented
6C47×#1443C211yesmaximal, characteristic, complemented
7C47×#1440C211yesmaximal, characteristic, complemented
8C47×#1440C211yesmaximal, characteristic, complemented
9C47×#1439C211yesmaximal, characteristic, complemented
10C47×#1439C211yesmaximal, characteristic, complemented
11C47×#1438C211yesmaximal, characteristic, complemented
12C47×#1438C211yesmaximal, characteristic, complemented
13C47×#1438C211yesmaximal, characteristic, complemented
14C47×#1438C211yesmaximal, characteristic, complemented
15C47×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C23×D4×C47C2211yescharacteristic
19C24×C4×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C22⋊C4×C47C2211yescharacteristic
22C22×C22⋊C4×C47C2211yescharacteristic
23C22×C22⋊C4×C47C2211yescharacteristic
24C22×C22⋊C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47C2211yescharacteristic
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2211yescharacteristic
28C22×C22⋊C4×C47C2211yescharacteristic
29C22×C22⋊C4×C47C2211yescharacteristic
30C22×C22⋊C4×C47C2211yescharacteristic
31C22×C22⋊C4×C47C2211yescharacteristic
32C22×C22⋊C4×C47C2211yescharacteristic
33C22×C22⋊C4×C47C2211yescharacteristic
34C22×C22⋊C4×C47C2211yescharacteristic
35C47×#397—24no—
36C47×#392—24no—
37C47×#386—24no—
38C47×#386—24no—
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2211yescharacteristic
41C2×#95×C47C2211yescharacteristic
42C2×#95×C47C2211yescharacteristic
43C2×#95×C47C2211yescharacteristic
44C2×#95×C47C2211yescharacteristic
45C2×#95×C47C2211yescharacteristic
46C2×#95×C47C2211yescharacteristic
47C2×#95×C47C2211yescharacteristic
48C2×#95×C47C2211yescharacteristic
49C2×#95×C47C2211yescharacteristic
50C2×#95×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C25×C47C2311yescharacteristic
56C25×C47C2311yescharacteristic
57C25×C47C2311yescharacteristic
58C22×D4×C47—22no—
59C22×D4×C47—22no—
60C22×D4×C47—22no—
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—22no—
68C22×D4×C47—41no—
69C22×D4×C47—41no—
70C22×D4×C47—41no—
71C22×D4×C47—41no—
72C22×D4×C47—41no—
73C22×D4×C47—41no—
74C22×D4×C47—41no—
75C22×D4×C47—41no—
76C22×D4×C47—41no—
77C22×D4×C47—41no—
78C22×D4×C47D414yes—
79C23×C4×C47—22no—
80C23×C4×C47—22no—
81C23×C4×C47—22no—
82C23×C4×C47—41no—
83C23×C4×C47—41no—
84C23×C4×C47—41no—
85C23×C4×C47—41no—
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2311yescharacteristic
94C23×C4×C47C2311yescharacteristic
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47—22no—
99C2×C4⋊C4×C47—41no—
100C2×C4⋊C4×C47—41no—
101C2×C22⋊C4×C47—22no—
102C2×C22⋊C4×C47—22no—
103C2×C22⋊C4×C47—22no—
104C2×C22⋊C4×C47—22no—
105C2×C22⋊C4×C47—22no—
106C2×C22⋊C4×C47—22no—
107C2×C22⋊C4×C47—22no—
108C2×C22⋊C4×C47—22no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—22no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47—22no—
114C2×C22⋊C4×C47—22no—
115C2×C22⋊C4×C47—22no—
116C2×C22⋊C4×C47—22no—
117C2×C22⋊C4×C47—22no—
118C2×C22⋊C4×C47—22no—
119C2×C22⋊C4×C47—41no—
120C2×C22⋊C4×C47—41no—
121C2×C22⋊C4×C47—41no—
122C2×C22⋊C4×C47—41no—
123C2×C22⋊C4×C47—41no—
124C2×C22⋊C4×C47—41no—
125C2×C22⋊C4×C47—41no—
126C2×C22⋊C4×C47—41no—
127C2×C22⋊C4×C47—41no—
128C2×C22⋊C4×C47—41no—
129C2×C22⋊C4×C47—41no—
130C2×C22⋊C4×C47—41no—
131C2×C22⋊C4×C47—41no—
132C2×C22⋊C4×C47—41no—
133C2×C22⋊C4×C47—41no—
134C2×C22⋊C4×C47—41no—
135C2×C22⋊C4×C47—41no—
136C2×C22⋊C4×C47—41no—
137C2×C22⋊C4×C47—41no—
138C2×C22⋊C4×C47—41no—
139C2×C22⋊C4×C47—41no—
140C2×C22⋊C4×C47—41no—
141C2×C22⋊C4×C47—41no—
142C2×C22⋊C4×C47—41no—
143#95×C47—22no—
144#95×C47—22no—
145#95×C47—22no—
146#95×C47—22no—
147#95×C47—22no—
148#95×C47—22no—
149#95×C47—22no—
150#95×C47—41no—
151#95×C47—41no—
152#95×C47—41no—
153#95×C47—41no—
154#95×C47—41no—
155#95×C47—41no—
156#95×C47—41no—
157#95×C47—41no—
158#95×C47D414yescomplemented
159C24×C47—21no—
160C24×C47—21no—
161C24×C47—21no—
162C24×C47—21no—
163C24×C47—21no—
164C24×C47—21no—
165C24×C47—21no—
166C24×C47—21no—
167C24×C47—21no—
168C24×C47—21no—
169C24×C47—21no—
170C24×C47—21no—
171C24×C47—21no—
172C24×C47—21no—
173C24×C47—21no—
174C24×C47—21no—
175C24×C47—21no—
176C24×C47—21no—
177C24×C47—21no—
178C24×C47—21no—
179C24×C47—21no—
180C24×C47—21no—
181C24×C47—21no—
182C24×C47—21no—
183C24×C47—21no—
184C24×C47—21no—
185C24×C47—21no—
186C24×C47—21no—
187C24×C47—21no—
188C24×C47—21no—
189C24×C47—21no—
190C24×C47—21no—
191C24×C47—21no—
192C24×C47—21no—
193C24×C47—21no—
194C24×C47—21no—
195C24×C47—21no—
196C24×C47—21no—
197C24×C47—21no—
198C24×C47—21no—
199C24×C47C2×D412yes—
200C24×C47C2×D412yes—
201C24×C47#4112yes—
202C24×C47#4112yes—
203C24×C47#4112yes—
204C24×C47C2411yescharacteristic
205C2×D4×C47—28no—
206C2×D4×C47—28no—
207C2×D4×C47—44no—
208C2×D4×C47—44no—
209C2×D4×C47—44no—
210C2×D4×C47—44no—
211C2×D4×C47—44no—
212C2×D4×C47—44no—
213C2×D4×C47—44no—
214C2×D4×C47—44no—
215C2×D4×C47—44no—
216C2×D4×C47—44no—
217C2×D4×C47—44no—
218C2×D4×C47—44no—
219C2×D4×C47—44no—
220C2×D4×C47—44no—
221C2×D4×C47—44no—
222C2×D4×C47—44no—
223C2×D4×C47—44no—
224C2×D4×C47—44no—
225C2×D4×C47—44no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—21no—
241C22×C4×C47—21no—
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—21no—
258C22×C4×C47—21no—
259C22×C4×C47—21no—
260C22×C4×C47—21no—
261C22×C4×C47—21no—
262C22×C4×C47—21no—
263C22×C4×C47—21no—
264C22×C4×C47—21no—
265C22×C4×C47—21no—
266C22×C4×C47—21no—
267C22×C4×C47—21no—
268C22×C4×C47—21no—
269C22×C4×C47—21no—
270C22×C4×C47—21no—
271C22×C4×C47—21no—
272C22×C4×C47—21no—
273C22×C4×C47—21no—
274C22×C4×C47—21no—
275C22×C4×C47—21no—
276C22×C4×C47—21no—
277C22×C4×C47—21no—
278C22×C4×C47—21no—
279C22×C4×C47—21no—
280C22×C4×C47—21no—
281C22×C4×C47—21no—
282C22×C4×C47—21no—
283C22×C4×C47—21no—
284C22×C4×C47—21no—
285C22×C4×C47—21no—
286C22×C4×C47—21no—
287C22×C4×C47—21no—
288C22×C4×C47—21no—
289C22×C4×C47—21no—
290C22×C4×C47—21no—
291C22×C4×C47—21no—
292C22×C4×C47—21no—
293C22×C4×C47—21no—
294C22×C4×C47—21no—
295C22×C4×C47—21no—
296C22×C4×C47—21no—
297C22×C4×C47—21no—
298C22×C4×C47—21no—
299C22×C4×C47—21no—
300C22×C4×C47—21no—
301C22×C4×C47—21no—
302C22×C4×C47—21no—
303C22×C4×C47—21no—
304C22×C4×C47—44no—
305C22×C4×C47—44no—
306C22×C4×C47—44no—
307C22×C4×C47—44no—
308C22×C4×C47—44no—
309C22×C4×C47—44no—
310C22×C4×C47—44no—
311C22×C4×C47C2×D412yes—
312C22×C4×C47C2×D412yes—
313C22×C4×C47C2×D412yes—
314C22×C4×C47C2×D412yes—
315C22×C4×C47#4112yes—
316C22×C4×C47#4112yes—
317C4⋊C4×C47—44no—
318C22⋊C4×C47—44no—
319C22⋊C4×C47—44no—
320C22⋊C4×C47—44no—
321C22⋊C4×C47—44no—
322C22⋊C4×C47—44no—
323C22⋊C4×C47—44no—
324C22⋊C4×C47—44no—
325C22⋊C4×C47—44no—
326C22⋊C4×C47—44no—
327C22⋊C4×C47—44no—
328C22⋊C4×C47—44no—
329C22⋊C4×C47—44no—
330C22⋊C4×C47—44no—
331C22⋊C4×C47—44no—
332C23×C47—22no—
333C23×C47—22no—
334C23×C47—22no—
335C23×C47—22no—
336C23×C47—22no—
337C23×C47—22no—
338C23×C47—22no—
339C23×C47—22no—
340C23×C47—22no—
341C23×C47—22no—
342C23×C47—22no—
343C23×C47—22no—
344C23×C47—22no—
345C23×C47—22no—
346C23×C47—22no—
347C23×C47—22no—
348C23×C47—22no—
349C23×C47—22no—
350C23×C47—22no—
351C23×C47—22no—
352C23×C47—22no—
353C23×C47—22no—
354C23×C47—22no—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—22no—
358C23×C47—22no—
359C23×C47—22no—
360C23×C47—22no—
361C23×C47—22no—
362C23×C47—22no—
363C23×C47—22no—
364C23×C47—41no—
365C23×C47—41no—
366C23×C47—41no—
367C23×C47—41no—
368C23×C47—41no—
369C23×C47—41no—
370C23×C47—41no—
371C23×C47—41no—
372C23×C47—41no—
373C23×C47—41no—
374C23×C47—41no—
375C23×C47—41no—
376C23×C47—41no—
377C23×C47—41no—
378C23×C47—41no—
379C23×C47—41no—
380C23×C47—41no—
381C23×C47—41no—
382C23×C47—41no—
383C23×C47—41no—
384C23×C47—41no—
385C23×C47—41no—
386C23×C47—41no—
387C23×C47—41no—
388C23×C47—41no—
389C23×C47—41no—
390C23×C47—41no—
391C23×C47—41no—
392C23×C47—41no—
393C23×C47—41no—
394C23×C47—41no—
395C23×C47—41no—
396C23×C47—41no—
397C23×C47—41no—
398C23×C47—41no—
399C23×C47—41no—
400C23×C47—41no—
401C23×C47—41no—
402C23×C47—41no—
403C23×C47—41no—
404C23×C47—41no—
405C23×C47—41no—
406C23×C47—41no—
407C23×C47—41no—
408C23×C47—41no—
409C23×C47—41no—
410C23×C47—41no—
411C23×C47—41no—
412C23×C47—41no—
413C23×C47—41no—
414C23×C47—41no—
415C23×C47—41no—
416C23×C47—41no—
417C23×C47—41no—
418C23×C47—41no—
419C23×C47—41no—
420C23×C47—41no—
421C23×C47—41no—
422C23×C47—41no—
423C23×C47—41no—
424C23×C47—41no—
425C23×C47—41no—
426C23×C47—41no—
427C23×C47—41no—
428C23×C47—41no—
429C23×C47—41no—
430C23×C47—41no—
431C23×C47—41no—
432C23×C47—41no—
433C23×C47—41no—
434C23×C47—41no—
435C23×C47—41no—
436C23×C47#12314yes—
437C23×C47C22×D411yescharacteristic
438C23×C47C22×D411yescharacteristic
439C23×C47C2×#4111yescharacteristic
440C23×C47C2×#4111yescharacteristic
441C23×C47C2×#4111yescharacteristic
442C23×C47C2×#4111yescharacteristic
443C23×C47C2×#4111yescharacteristic
444C23×C47H(5,𝔽2)11yescharacteristic
445C23×C47H(5,𝔽2)11yescharacteristic
446C23×C47H(5,𝔽2)11yescharacteristic
447C23×C47H(5,𝔽2)11yescharacteristic
448C23×C47H(5,𝔽2)11yescharacteristic
449C23×C47H(5,𝔽2)11yescharacteristic
450C23×C47H(5,𝔽2)11yescharacteristic
451C23×C47H(5,𝔽2)11yescharacteristic
452D4×C47—416no—
453D4×C47—416no—
454D4×C47—416no—
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—22no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—22no—
473C2×C4×C47—416no—
474C2×C4×C47—41no—
475C2×C4×C47—41no—
476C2×C4×C47—41no—
477C2×C4×C47—41no—
478C2×C4×C47—41no—
479C2×C4×C47—41no—
480C2×C4×C47—41no—
481C2×C4×C47—41no—
482C2×C4×C47—41no—
483C2×C4×C47—41no—
484C2×C4×C47—41no—
485C2×C4×C47—41no—
486C2×C4×C47—41no—
487C2×C4×C47—41no—
488C2×C4×C47—41no—
489C2×C4×C47—41no—
490C2×C4×C47—41no—
491C2×C4×C47—41no—
492C2×C4×C47—41no—
493C2×C4×C47—41no—
494C2×C4×C47—41no—
495C2×C4×C47—41no—
496C2×C4×C47—41no—
497C2×C4×C47—41no—
498C2×C4×C47—41no—
499C2×C4×C47—41no—
500C2×C4×C47—41no—
501C2×C4×C47—41no—
502C2×C4×C47—41no—
503C2×C4×C47—41no—
504C2×C4×C47—41no—
505C2×C4×C47—41no—
506C2×C4×C47—41no—
507C2×C4×C47—41no—
508C2×C4×C47—41no—
509C2×C4×C47—41no—
510C2×C4×C47—41no—
511C2×C4×C47—41no—
512C2×C4×C47—41no—
513C2×C4×C47—41no—
514C2×C4×C47—41no—
515C2×C4×C47—41no—
516C2×C4×C47—41no—
517C2×C4×C47—41no—
518C2×C4×C47—41no—
519C2×C4×C47—41no—
520C2×C4×C47—41no—
521C2×C4×C47—41no—
522C2×C4×C47—41no—
523C2×C4×C47—41no—
524C2×C4×C47—41no—
525C2×C4×C47—41no—
526C2×C4×C47—41no—
527C2×C4×C47—41no—
528C2×C4×C47—41no—
529C2×C4×C47—41no—
530C2×C4×C47—41no—
531C2×C4×C47—41no—
532C2×C4×C47—41no—
533C2×C4×C47—41no—
534C2×C4×C47—41no—
535C2×C4×C47—41no—
536C2×C4×C47—41no—
537C2×C4×C47—41no—
538C2×C4×C47—41no—
539C2×C4×C47—41no—
540#16270C4711yesmaximal, characteristic, direct product factor, Sylow
541C22×C47—24no—
542C22×C47—24no—
543C22×C47—24no—
544C22×C47—42no—
545C22×C47—42no—
546C22×C47—42no—
547C22×C47—42no—
548C22×C47—42no—
549C22×C47—42no—
550C22×C47—42no—
551C22×C47—42no—
552C22×C47—42no—
553C22×C47—42no—
554C22×C47—42no—
555C22×C47—42no—
556C22×C47—42no—
557C22×C47—42no—
558C22×C47—42no—
559C22×C47—42no—
560C22×C47—42no—
561C22×C47—42no—
562C22×C47—42no—
563C22×C47—42no—
564C22×C47—42no—
565C22×C47—42no—
566C22×C47—42no—
567C22×C47—42no—
568C22×C47—42no—
569C22×C47—42no—
570C22×C47—81no—
571C22×C47—81no—
572C22×C47—81no—
573C22×C47—81no—
574C22×C47—81no—
575C22×C47—81no—
576C22×C47—81no—
577C22×C47—81no—
578C22×C47—81no—
579C22×C47—81no—
580C22×C47—81no—
581C22×C47—81no—
582C22×C47—81no—
583C22×C47—81no—
584C22×C47—81no—
585C22×C47—81no—
586C22×C47C2×#12311yescharacteristic
587C22×C47#52511yescharacteristic
588C22×C47#52911yescharacteristic
589C22×C47#53411yescharacteristic
590C22×C47#53411yescharacteristic
591C22×C47#53511yescharacteristic
592C22×C47#53511yescharacteristic
593C22×C47#53811yescharacteristic
594C22×C47#53811yescharacteristic
595C22×C47#53811yescharacteristic
596C22×C47#53811yescharacteristic
597C22×C47#53811yescharacteristic
598C22×C47#53811yescharacteristic
599C22×C47#53811yescharacteristic
600C22×C47#53811yescharacteristic
601C22×C47#53811yescharacteristic
602C22×C47#53811yescharacteristic
603C22×C47#54011yescharacteristic
604C22×C47#54011yescharacteristic
605C22×C47D4211yescharacteristic
606C22×C47#54611yescharacteristic
607C22×C47#54611yescharacteristic
608C22×C47#54611yescharacteristic
609C22×C47#54611yescharacteristic
610C22×C47#54611yescharacteristic
611C22×C47#55011yescharacteristic
612C22×C47#55111yescharacteristic
613C22×C47#55111yescharacteristic
614C22×C47#55311yescharacteristic
615C22×C47#55311yescharacteristic
616C22×C47#55311yescharacteristic
617C22×C47#56011yescharacteristic
618C22×C47#56011yescharacteristic
619C22×C47#56011yescharacteristic
620C22×C47#56011yescharacteristic
621C4×C47—42no—
622C4×C47—42no—
623C4×C47—42no—
624C4×C47—42no—
625C4×C47—42no—
626C4×C47—42no—
627C4×C47—81no—
628C4×C47—81no—
629C4×C47—81no—
630C4×C47—81no—
631C4×C47—81no—
632C4×C47—81no—
633C2×#397C2×C4711yescharacteristic, complemented
634C2×#392C2×C4711yescharacteristic
635C2×#386C2×C4711yescharacteristic, complemented
636C2×#386C2×C4711yescharacteristic, complemented
637#1443C2×C4711yescharacteristic, complemented
638#1443C2×C4711yescharacteristic, complemented
639#1440C2×C4711yescharacteristic, complemented
640#1440C2×C4711yescharacteristic, complemented
641#1439C2×C4711yescharacteristic, complemented
642#1439C2×C4711yescharacteristic, complemented
643#1438C2×C4711yescharacteristic, complemented
644#1438C2×C4711yescharacteristic, complemented
645#1438C2×C4711yescharacteristic, complemented
646#1438C2×C4711yescharacteristic, complemented
647C22⋊#95C2×C4711yescharacteristic, complemented
648C2×C47—44no—
649C2×C47—82no—
650C2×C47—82no—
651C2×C47#241811yescharacteristic
652C2×C47#244411yescharacteristic
653C2×C47#246711yescharacteristic
654C2×C47#262211yescharacteristic
655C2×C47#263111yescharacteristic
656C2×C47#264811yescharacteristic
657C2×C47#267311yescharacteristic
658C2×C47#267811yescharacteristic
659C2×C47#268811yescharacteristic
660C2×C47#269711yescharacteristic
661C2×C47#270311yescharacteristic
662C2×C47#271411yescharacteristic
663C2×C47#274911yescharacteristic
664C2×C47#277811yescharacteristic
665C2×C47#282511yescharacteristic
666C23×D4C22×C4711yescharacteristic
667C23×D4C22×C4711yescharacteristic
668C23×D4C22×C4711yescharacteristic
669C24×C4C22×C4711yescharacteristic
670C22×C4⋊C4C22×C4711yescharacteristic
671C22×C22⋊C4C22×C4711yescharacteristic
672C22×C22⋊C4C22×C4711yescharacteristic
673C22×C22⋊C4C22×C4711yescharacteristic
674C22×C22⋊C4C22×C4711yescharacteristic
675C22×C22⋊C4C22×C4711yescharacteristic
676C22×C22⋊C4C22×C4711yescharacteristic
677C22×C22⋊C4C22×C4711yescharacteristic
678C22×C22⋊C4C22×C4711yescharacteristic
679C22×C22⋊C4C22×C4711yescharacteristic
680C22×C22⋊C4C22×C4711yescharacteristic
681C22×C22⋊C4C22×C4711yescharacteristic
682C22×C22⋊C4C22×C4711yescharacteristic
683C22×C22⋊C4C22×C4711yescharacteristic
684C22×C22⋊C4C22×C4711yescharacteristic
685#397—24no—
686#392—24no—
687#386—24no—
688#386—24no—
689C2×#95C22×C4711yescharacteristic
690C2×#95C22×C4711yescharacteristic
691C2×#95C22×C4711yescharacteristic
692C2×#95C22×C4711yescharacteristic
693C2×#95C22×C4711yescharacteristic
694C2×#95C22×C4711yescharacteristic
695C2×#95C22×C4711yescharacteristic
696C2×#95C22×C4711yescharacteristic
697C2×#95C22×C4711yescharacteristic
698C2×#95C22×C4711yescharacteristic
699C2×#95C22×C4711yescharacteristic
700C2×#95C22×C4711yescharacteristic
701C2×#95C22×C4711yescharacteristic
702C2×#95C22×C4711yescharacteristic
703C2×#95C22×C4711yescharacteristic
704C2×#95C22×C4711yescharacteristic
705C47#1627011yescharacteristic, direct product factor, Sylow
706C25C23×C4711yescharacteristic
707C25C23×C4711yescharacteristic
708C25C23×C4711yescharacteristic
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4D4×C4714yes—
730C23×C4—22no—
731C23×C4—22no—
732C23×C4—22no—
733C23×C4—41no—
734C23×C4—41no—
735C23×C4—41no—
736C23×C4—41no—
737C23×C4C23×C4711yescharacteristic
738C23×C4C23×C4711yescharacteristic
739C23×C4C23×C4711yescharacteristic
740C23×C4C23×C4711yescharacteristic
741C23×C4C23×C4711yescharacteristic
742C23×C4C23×C4711yescharacteristic
743C23×C4C23×C4711yescharacteristic
744C23×C4C23×C4711yescharacteristic
745C23×C4C23×C4711yescharacteristic
746C23×C4C23×C4711yescharacteristic
747C23×C4C23×C4711yescharacteristic
748C23×C4C23×C4711yescharacteristic
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C4⋊C4—41no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95—41no—
805#95—41no—
806#95—41no—
807#95—41no—
808#95—41no—
809#95D4×C4714yescomplemented
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24C2×D4×C4712yes—
851C24C2×D4×C4712yes—
852C24#41×C4712yes—
853C24#41×C4712yes—
854C24#41×C4712yes—
855C24C24×C4711yescharacteristic
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4C2×D4×C4712yes—
963C22×C4C2×D4×C4712yes—
964C22×C4C2×D4×C4712yes—
965C22×C4C2×D4×C4712yes—
966C22×C4#41×C4712yes—
967C22×C4#41×C4712yes—
968C4⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23#123×C4714yes—
1088C23C22×D4×C4711yescharacteristic
1089C23C22×D4×C4711yescharacteristic
1090C23C2×#41×C4711yescharacteristic
1091C23C2×#41×C4711yescharacteristic
1092C23C2×#41×C4711yescharacteristic
1093C23C2×#41×C4711yescharacteristic
1094C23C2×#41×C4711yescharacteristic
1095C23H(5,𝔽2)×C4711yescharacteristic
1096C23H(5,𝔽2)×C4711yescharacteristic
1097C23H(5,𝔽2)×C4711yescharacteristic
1098C23H(5,𝔽2)×C4711yescharacteristic
1099C23H(5,𝔽2)×C4711yescharacteristic
1100C23H(5,𝔽2)×C4711yescharacteristic
1101C23H(5,𝔽2)×C4711yescharacteristic
1102C23H(5,𝔽2)×C4711yescharacteristic
1103D4—416no—
1104D4—416no—
1105D4—416no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—416no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22C2×#123×C4711yescharacteristic
1237C22C47×#52511yescharacteristic
1238C22C47×#52911yescharacteristic
1239C22C47×#53411yescharacteristic
1240C22C47×#53411yescharacteristic
1241C22C47×#53511yescharacteristic
1242C22C47×#53511yescharacteristic
1243C22C47×#53811yescharacteristic
1244C22C47×#53811yescharacteristic
1245C22C47×#53811yescharacteristic
1246C22C47×#53811yescharacteristic
1247C22C47×#53811yescharacteristic
1248C22C47×#53811yescharacteristic
1249C22C47×#53811yescharacteristic
1250C22C47×#53811yescharacteristic
1251C22C47×#53811yescharacteristic
1252C22C47×#53811yescharacteristic
1253C22C47×#54011yescharacteristic
1254C22C47×#54011yescharacteristic
1255C22D42×C4711yescharacteristic
1256C22C47×#54611yescharacteristic
1257C22C47×#54611yescharacteristic
1258C22C47×#54611yescharacteristic
1259C22C47×#54611yescharacteristic
1260C22C47×#54611yescharacteristic
1261C22C47×#55011yescharacteristic
1262C22C47×#55111yescharacteristic
1263C22C47×#55111yescharacteristic
1264C22C47×#55311yescharacteristic
1265C22C47×#55311yescharacteristic
1266C22C47×#55311yescharacteristic
1267C22C47×#56011yescharacteristic
1268C22C47×#56011yescharacteristic
1269C22C47×#56011yescharacteristic
1270C22C47×#56011yescharacteristic
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C2—44no—
1284C2—82no—
1285C2—82no—
1286C2C47×#241811yescharacteristic
1287C2C47×#244411yescharacteristic
1288C2C47×#246711yescharacteristic
1289C2C47×#262211yescharacteristic
1290C2C47×#263111yescharacteristic
1291C2C47×#264811yescharacteristic
1292C2C47×#267311yescharacteristic
1293C2C47×#267811yescharacteristic
1294C2C47×#268811yescharacteristic
1295C2C47×#269711yescharacteristic
1296C2C47×#270311yescharacteristic
1297C2C47×#271411yescharacteristic
1298C2C47×#274911yescharacteristic
1299C2C47×#277811yescharacteristic
1300C2C47×#282511yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC24C24×C47
prime radicalC2×C47×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#397C2semidirect
3. C2×C47×#386C2semidirect
4. C2×C47×#386C2semidirect
5. C47×#1443C2semidirect
6. C47×#1443C2semidirect
7. C47×#1440C2semidirect
8. C47×#1440C2semidirect
9. C47×#1439C2semidirect
10. C47×#1439C2semidirect
11. C47×#1438C2semidirect
12. C47×#1438C2semidirect
13. C47×#1438C2semidirect
14. C47×#1438C2semidirect
15. C47×C22⋊#95C2semidirect
158. #95×C47D4semidirect
540. #16270C47direct (N × H)
633. C2×#397C2×C47semidirect
635. C2×#386C2×C47semidirect
636. C2×#386C2×C47semidirect
637. #1443C2×C47semidirect
638. #1443C2×C47semidirect
639. #1440C2×C47semidirect
640. #1440C2×C47semidirect
641. #1439C2×C47semidirect
642. #1439C2×C47semidirect
643. #1438C2×C47semidirect
644. #1438C2×C47semidirect
645. #1438C2×C47semidirect
646. #1438C2×C47semidirect
647. C22⋊#95C2×C47semidirect
705. C47#16270direct (N × H)
809. #95D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#3972
C2×C47×#3922
C2×C47×#3862
C47×#14432
C47×#14402
C47×#14392
C47×#14382
C47×C22⋊#952
#1627047