Finite Group Databasebeta

← C47×#14519 #26054217

Subgroups — C47×#14519 #26054217

Order 12032.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#392C211yesmaximal, characteristic
2C2×C47×#390C211yesmaximal, characteristic, complemented
3C2×C47×#386C211yesmaximal, characteristic, complemented
4C2×C47×#386C211yesmaximal, characteristic, complemented
5C2×C47×#386C211yesmaximal, characteristic, complemented
6C2×C47×#386C211yesmaximal, characteristic, complemented
7C2×C47×#385C211yesmaximal, characteristic, complemented
8C47×#1442C211yesmaximal, characteristic, complemented
9C47×#1440C211yesmaximal, characteristic, complemented
10C47×#1439C211yesmaximal, characteristic, complemented
11C47×#1439C211yesmaximal, characteristic, complemented
12C47×#1438C211yesmaximal, characteristic, complemented
13C47×#1437C211yesmaximal, characteristic, complemented
14C47×#1434C211yesmaximal, characteristic, complemented
15C47×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C23×D4×C47C2211yescharacteristic
19C24×C4×C47C2211yescharacteristic
20C24×C4×C47C2211yescharacteristic
21C22×C4⋊C4×C47C2211yescharacteristic
22C22×C4⋊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
35C22×C22⋊C4×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C47×#392C418yescomplemented
38C47×#390—24no—
39C47×#386—24no—
40C47×#386—24no—
41C47×#386—24no—
42C47×#386—24no—
43C47×#385—24no—
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
55C2×#95×C47C2211yescharacteristic
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C25×C47C2311yescharacteristic
59C25×C47C2311yescharacteristic
60C25×C47C2311yescharacteristic
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—22no—
69C22×D4×C47—22no—
70C22×D4×C47—22no—
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×C47—41no—
79C22×D4×C47C2×C414yes—
80C22×D4×C47C2×C414yescomplemented
81C22×D4×C47C2×C414yescomplemented
82C23×C4×C47—22no—
83C23×C4×C47—22no—
84C23×C4×C47—22no—
85C23×C4×C47—22no—
86C23×C4×C47—22no—
87C23×C4×C47—22no—
88C23×C4×C47—41no—
89C23×C4×C47—41no—
90C23×C4×C47—41no—
91C23×C4×C47—41no—
92C23×C4×C47—41no—
93C23×C4×C47—41no—
94C23×C4×C47—41no—
95C23×C4×C47—41no—
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2311yescharacteristic
100C23×C4×C47C2311yescharacteristic
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47—22no—
109C2×C4⋊C4×C47—22no—
110C2×C4⋊C4×C47—22no—
111C2×C4⋊C4×C47—41no—
112C2×C4⋊C4×C47—41no—
113C2×C4⋊C4×C47—41no—
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—22no—
120C2×C22⋊C4×C47—22no—
121C2×C22⋊C4×C47—22no—
122C2×C22⋊C4×C47—22no—
123C2×C22⋊C4×C47—22no—
124C2×C22⋊C4×C47—22no—
125C2×C22⋊C4×C47—22no—
126C2×C22⋊C4×C47—22no—
127C2×C22⋊C4×C47—22no—
128C2×C22⋊C4×C47—22no—
129C2×C22⋊C4×C47—22no—
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—
143C2×C22⋊C4×C47—41no—
144C2×C22⋊C4×C47—41no—
145C2×C22⋊C4×C47—41no—
146C2×C22⋊C4×C47—41no—
147C2×C22⋊C4×C47—41no—
148C2×C22⋊C4×C47C2×C414yescomplemented
149C2×C22⋊C4×C47C2×C414yescomplemented
150C2×C22⋊C4×C47C2×C414yescomplemented
151C2×C22⋊C4×C47D414yescomplemented
152C2×C22⋊C4×C47D414yescomplemented
153C2×C42×C47—22no—
154C2×C42×C47—22no—
155C2×C42×C47—41no—
156#95×C47—22no—
157#95×C47—22no—
158#95×C47—22no—
159#95×C47—22no—
160#95×C47—22no—
161#95×C47—22no—
162#95×C47—22no—
163#95×C47—22no—
164#95×C47—41no—
165#95×C47—41no—
166#95×C47—41no—
167#95×C47—41no—
168#95×C47C2×C414yescomplemented
169#95×C47D414yescomplemented
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×C47—21no—
200C24×C47—21no—
201C24×C47—21no—
202C24×C47—21no—
203C24×C47—21no—
204C24×C47—21no—
205C24×C47—21no—
206C24×C47—21no—
207C24×C47—21no—
208C24×C47C22×C412yes—
209C24×C47C22×C412yes—
210C24×C47C22×C412yes—
211C24×C47C2×D412yes—
212C24×C47C2×D412yes—
213C24×C47#4112yes—
214C24×C47#4112yes—
215C24×C47C2411yescharacteristic
216C2×D4×C47—28no—
217C2×D4×C47—28no—
218C2×D4×C47—28no—
219C2×D4×C47—28no—
220C2×D4×C47—28no—
221C2×D4×C47—44no—
222C2×D4×C47—44no—
223C2×D4×C47—44no—
224C2×D4×C47—44no—
225C2×D4×C47—44no—
226C2×D4×C47—44no—
227C2×D4×C47—44no—
228C2×D4×C47—44no—
229C2×D4×C47—44no—
230C2×D4×C47—44no—
231C2×D4×C47—44no—
232C2×D4×C47—44no—
233C2×D4×C47—44no—
234C2×D4×C47—44no—
235C2×D4×C47—44no—
236C2×D4×C47—44no—
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—21no—
305C22×C4×C47—21no—
306C22×C4×C47—21no—
307C22×C4×C47—21no—
308C22×C4×C47—21no—
309C22×C4×C47—44no—
310C22×C4×C47—44no—
311C22×C4×C47—44no—
312C22×C4×C47—44no—
313C22×C4×C47—44no—
314C22×C4×C47—44no—
315C22×C4×C47—44no—
316C22×C4×C47—44no—
317C22×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×C47C22×C412yes—
324C22×C4×C47C22×C412yes—
325C22×C4×C47C22×C412yes—
326C22×C4×C47C22×C412yes—
327C22×C4×C47C2×D412yes—
328C22×C4×C47C2×D412yes—
329C22×C4×C47C2×D412yes—
330C22×C4×C47C2×D412yes—
331C22×C4×C47C2×D412yes—
332C22×C4×C47C2×D412yes—
333C22×C4×C47C2×D412yes—
334C22×C4×C47#4112yes—
335C4⋊C4×C47—44no—
336C4⋊C4×C47—44no—
337C22⋊C4×C47—28no—
338C22⋊C4×C47—44no—
339C22⋊C4×C47—44no—
340C22⋊C4×C47—44no—
341C22⋊C4×C47—44no—
342C22⋊C4×C47—44no—
343C22⋊C4×C47—44no—
344C22⋊C4×C47—44no—
345C22⋊C4×C47—44no—
346C22⋊C4×C47—44no—
347C22⋊C4×C47—44no—
348C22⋊C4×C47—44no—
349C22⋊C4×C47—44no—
350C42×C47—44no—
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—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—22no—
387C23×C47—22no—
388C23×C47—22no—
389C23×C47—22no—
390C23×C47—22no—
391C23×C47—22no—
392C23×C47—22no—
393C23×C47—22no—
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—41no—
437C23×C47—41no—
438C23×C47—41no—
439C23×C47—41no—
440C23×C47—41no—
441C23×C47—41no—
442C23×C47—41no—
443C23×C47—41no—
444C23×C47—41no—
445C23×C47—41no—
446C23×C47—41no—
447C23×C47—41no—
448C23×C47—41no—
449C23×C47—41no—
450C23×C47—41no—
451C23×C47—41no—
452C23×C47—41no—
453C23×C47—41no—
454C23×C47C4×D414yes—
455C23×C47C4×D414yes—
456C23×C47C23×C411yescharacteristic
457C23×C47C22×D411yescharacteristic
458C23×C47C22×D411yescharacteristic
459C23×C47C22×D411yescharacteristic
460C23×C47C2×#4111yescharacteristic
461C23×C47C2×#4111yescharacteristic
462C23×C47C2×#4111yescharacteristic
463C23×C47H(5,𝔽2)11yescharacteristic
464C23×C47H(5,𝔽2)11yescharacteristic
465C23×C47H(5,𝔽2)11yescharacteristic
466C23×C47H(5,𝔽2)11yescharacteristic
467C23×C47H(5,𝔽2)11yescharacteristic
468C23×C47H(5,𝔽2)11yescharacteristic
469C23×C47H(5,𝔽2)11yescharacteristic
470C23×C472−1+411yescharacteristic
471D4×C47—416no—
472D4×C47—416no—
473D4×C47—416no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—22no—
477C2×C4×C47—22no—
478C2×C4×C47—22no—
479C2×C4×C47—22no—
480C2×C4×C47—22no—
481C2×C4×C47—22no—
482C2×C4×C47—22no—
483C2×C4×C47—22no—
484C2×C4×C47—22no—
485C2×C4×C47—22no—
486C2×C4×C47—22no—
487C2×C4×C47—22no—
488C2×C4×C47—22no—
489C2×C4×C47—22no—
490C2×C4×C47—22no—
491C2×C4×C47—22no—
492C2×C4×C47—22no—
493C2×C4×C47—22no—
494C2×C4×C47—22no—
495C2×C4×C47—22no—
496C2×C4×C47—22no—
497C2×C4×C47—22no—
498C2×C4×C47—22no—
499C2×C4×C47—22no—
500C2×C4×C47—22no—
501C2×C4×C47—22no—
502C2×C4×C47—22no—
503C2×C4×C47—22no—
504C2×C4×C47—22no—
505C2×C4×C47—22no—
506C2×C4×C47—22no—
507C2×C4×C47—416no—
508C2×C4×C47—416no—
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—
540C2×C4×C47—41no—
541C2×C4×C47—41no—
542C2×C4×C47—41no—
543C2×C4×C47—41no—
544C2×C4×C47—41no—
545C2×C4×C47—41no—
546C2×C4×C47—41no—
547C2×C4×C47—41no—
548C2×C4×C47—41no—
549C2×C4×C47—41no—
550C2×C4×C47—41no—
551C2×C4×C47—41no—
552C2×C4×C47—41no—
553C2×C4×C47—41no—
554C2×C4×C47—41no—
555C2×C4×C47—41no—
556C2×C4×C47—41no—
557C2×C4×C47—41no—
558C2×C4×C47—41no—
559C2×C4×C47C4×D414yes—
560#14519C4711yesmaximal, characteristic, direct product factor, Sylow
561C22×C47—24no—
562C22×C47—24no—
563C22×C47—24no—
564C22×C47—24no—
565C22×C47—24no—
566C22×C47—24no—
567C22×C47—42no—
568C22×C47—42no—
569C22×C47—42no—
570C22×C47—42no—
571C22×C47—42no—
572C22×C47—42no—
573C22×C47—42no—
574C22×C47—42no—
575C22×C47—42no—
576C22×C47—42no—
577C22×C47—42no—
578C22×C47—42no—
579C22×C47—42no—
580C22×C47—42no—
581C22×C47—42no—
582C22×C47—42no—
583C22×C47—42no—
584C22×C47—42no—
585C22×C47—42no—
586C22×C47—42no—
587C22×C47—42no—
588C22×C47—42no—
589C22×C47—42no—
590C22×C47—42no—
591C22×C47—42no—
592C22×C47—42no—
593C22×C47—42no—
594C22×C47—42no—
595C22×C47—42no—
596C22×C47—42no—
597C22×C47—42no—
598C22×C47—81no—
599C22×C47—81no—
600C22×C47—81no—
601C22×C47—81no—
602C22×C47—81no—
603C22×C47—81no—
604C22×C47—81no—
605C22×C47—81no—
606C22×C47C2×C4×D411yescharacteristic
607C22×C47C2×C4×D411yescharacteristic
608C22×C47C2×C4×D411yescharacteristic
609C22×C47#51811yescharacteristic
610C22×C47#51811yescharacteristic
611C22×C47#51811yescharacteristic
612C22×C47#52011yescharacteristic
613C22×C47#53411yescharacteristic
614C22×C47#53411yescharacteristic
615C22×C47#53511yescharacteristic
616C22×C47#53511yescharacteristic
617C22×C47#53511yescharacteristic
618C22×C47#53711yescharacteristic
619C22×C47#53811yescharacteristic
620C22×C47#53811yescharacteristic
621C22×C47#53811yescharacteristic
622C22×C47#53911yescharacteristic
623C22×C47#54011yescharacteristic
624C22×C47#54011yescharacteristic
625C22×C47D4211yescharacteristic
626C22×C47D4211yescharacteristic
627C22×C47D4211yescharacteristic
628C22×C47#54611yescharacteristic
629C22×C47#54611yescharacteristic
630C22×C47#54611yescharacteristic
631C22×C47#54611yescharacteristic
632C22×C47#54711yescharacteristic
633C22×C47#54811yescharacteristic
634C22×C47#55111yescharacteristic
635C22×C47#55111yescharacteristic
636C22×C47#55311yescharacteristic
637C22×C47#56011yescharacteristic
638C22×C47#56011yescharacteristic
639C22×C47#56211yescharacteristic
640C22×C47#56211yescharacteristic
641C4×C47—24no—
642C4×C47—42no—
643C4×C47—42no—
644C4×C47—42no—
645C4×C47—42no—
646C4×C47—42no—
647C4×C47—42no—
648C4×C47—42no—
649C4×C47—42no—
650C4×C47—42no—
651C4×C47—81no—
652C4×C47—81no—
653C2×#392C2×C4711yescharacteristic
654C2×#390C2×C4711yescharacteristic, complemented
655C2×#386C2×C4711yescharacteristic, complemented
656C2×#386C2×C4711yescharacteristic, complemented
657C2×#386C2×C4711yescharacteristic, complemented
658C2×#386C2×C4711yescharacteristic, complemented
659C2×#385C2×C4711yescharacteristic, complemented
660#1442C2×C4711yescharacteristic, complemented
661#1440C2×C4711yescharacteristic, complemented
662#1439C2×C4711yescharacteristic, complemented
663#1439C2×C4711yescharacteristic, complemented
664#1438C2×C4711yescharacteristic, complemented
665#1437C2×C4711yescharacteristic, complemented
666#1434C2×C4711yescharacteristic, complemented
667C22⋊#95C2×C4711yescharacteristic, complemented
668C2×C47—44no—
669C2×C47—44no—
670C2×C47—82no—
671C2×C47#232111yescharacteristic
672C2×C47#232511yescharacteristic
673C2×C47#232811yescharacteristic
674C2×C47#235811yescharacteristic
675C2×C47#235811yescharacteristic
676C2×C47#236111yescharacteristic
677C2×C47#237711yescharacteristic
678C2×C47#266911yescharacteristic
679C2×C47#267111yescharacteristic
680C2×C47#267611yescharacteristic
681C2×C47#267811yescharacteristic
682C2×C47#268811yescharacteristic
683C2×C47#269611yescharacteristic
684C2×C47#270611yescharacteristic
685C2×C47#274911yescharacteristic
686C23×D4C22×C4711yescharacteristic
687C23×D4C22×C4711yescharacteristic
688C23×D4C22×C4711yescharacteristic
689C24×C4C22×C4711yescharacteristic
690C24×C4C22×C4711yescharacteristic
691C22×C4⋊C4C22×C4711yescharacteristic
692C22×C4⋊C4C22×C4711yescharacteristic
693C22×C22⋊C4C22×C4711yescharacteristic
694C22×C22⋊C4C22×C4711yescharacteristic
695C22×C22⋊C4C22×C4711yescharacteristic
696C22×C22⋊C4C22×C4711yescharacteristic
697C22×C22⋊C4C22×C4711yescharacteristic
698C22×C22⋊C4C22×C4711yescharacteristic
699C22×C22⋊C4C22×C4711yescharacteristic
700C22×C22⋊C4C22×C4711yescharacteristic
701C22×C22⋊C4C22×C4711yescharacteristic
702C22×C22⋊C4C22×C4711yescharacteristic
703C22×C22⋊C4C22×C4711yescharacteristic
704C22×C22⋊C4C22×C4711yescharacteristic
705C22×C22⋊C4C22×C4711yescharacteristic
706C22×C42C22×C4711yescharacteristic
707#392C4×C4718yescomplemented
708#390—24no—
709#386—24no—
710#386—24no—
711#386—24no—
712#386—24no—
713#385—24no—
714C2×#95C22×C4711yescharacteristic
715C2×#95C22×C4711yescharacteristic
716C2×#95C22×C4711yescharacteristic
717C2×#95C22×C4711yescharacteristic
718C2×#95C22×C4711yescharacteristic
719C2×#95C22×C4711yescharacteristic
720C2×#95C22×C4711yescharacteristic
721C2×#95C22×C4711yescharacteristic
722C2×#95C22×C4711yescharacteristic
723C2×#95C22×C4711yescharacteristic
724C2×#95C22×C4711yescharacteristic
725C2×#95C22×C4711yescharacteristic
726C2×#95C22×C4711yescharacteristic
727C2×#95C22×C4711yescharacteristic
728C47#1451911yescharacteristic, direct product factor, Sylow
729C25C23×C4711yescharacteristic
730C25C23×C4711yescharacteristic
731C25C23×C4711yescharacteristic
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4C2×C4×C4714yes—
751C22×D4C2×C4×C4714yescomplemented
752C22×D4C2×C4×C4714yescomplemented
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—41no—
760C23×C4—41no—
761C23×C4—41no—
762C23×C4—41no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4C23×C4711yescharacteristic
768C23×C4C23×C4711yescharacteristic
769C23×C4C23×C4711yescharacteristic
770C23×C4C23×C4711yescharacteristic
771C23×C4C23×C4711yescharacteristic
772C23×C4C23×C4711yescharacteristic
773C23×C4C23×C4711yescharacteristic
774C23×C4C23×C4711yescharacteristic
775C23×C4C23×C4711yescharacteristic
776C23×C4C23×C4711yescharacteristic
777C23×C4C23×C4711yescharacteristic
778C23×C4C23×C4711yescharacteristic
779C2×C4⋊C4—22no—
780C2×C4⋊C4—22no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—41no—
783C2×C4⋊C4—41no—
784C2×C4⋊C4—41no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4C2×C4×C4714yescomplemented
820C2×C22⋊C4C2×C4×C4714yescomplemented
821C2×C22⋊C4C2×C4×C4714yescomplemented
822C2×C22⋊C4D4×C4714yescomplemented
823C2×C22⋊C4D4×C4714yescomplemented
824C2×C42—22no—
825C2×C42—22no—
826C2×C42—41no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—41no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95C2×C4×C4714yescomplemented
840#95D4×C4714yescomplemented
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24C22×C4×C4712yes—
880C24C22×C4×C4712yes—
881C24C22×C4×C4712yes—
882C24C2×D4×C4712yes—
883C24C2×D4×C4712yes—
884C24#41×C4712yes—
885C24#41×C4712yes—
886C24C24×C4711yescharacteristic
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
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—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4C22×C4×C4712yes—
995C22×C4C22×C4×C4712yes—
996C22×C4C22×C4×C4712yes—
997C22×C4C22×C4×C4712yes—
998C22×C4C2×D4×C4712yes—
999C22×C4C2×D4×C4712yes—
1000C22×C4C2×D4×C4712yes—
1001C22×C4C2×D4×C4712yes—
1002C22×C4C2×D4×C4712yes—
1003C22×C4C2×D4×C4712yes—
1004C22×C4C2×D4×C4712yes—
1005C22×C4#41×C4712yes—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C22⋊C4—28no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C42—44no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
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—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23C4×D4×C4714yes—
1126C23C4×D4×C4714yes—
1127C23C23×C4×C4711yescharacteristic
1128C23C22×D4×C4711yescharacteristic
1129C23C22×D4×C4711yescharacteristic
1130C23C22×D4×C4711yescharacteristic
1131C23C2×#41×C4711yescharacteristic
1132C23C2×#41×C4711yescharacteristic
1133C23C2×#41×C4711yescharacteristic
1134C23H(5,𝔽2)×C4711yescharacteristic
1135C23H(5,𝔽2)×C4711yescharacteristic
1136C23H(5,𝔽2)×C4711yescharacteristic
1137C23H(5,𝔽2)×C4711yescharacteristic
1138C23H(5,𝔽2)×C4711yescharacteristic
1139C23H(5,𝔽2)×C4711yescharacteristic
1140C23H(5,𝔽2)×C4711yescharacteristic
1141C232−1+4×C4711yescharacteristic
1142D4—416no—
1143D4—416no—
1144D4—416no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—416no—
1179C2×C4—416no—
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—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4C4×D4×C4714yes—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22C2×C4×D4×C4711yescharacteristic
1277C22C2×C4×D4×C4711yescharacteristic
1278C22C2×C4×D4×C4711yescharacteristic
1279C22C47×#51811yescharacteristic
1280C22C47×#51811yescharacteristic
1281C22C47×#51811yescharacteristic
1282C22C47×#52011yescharacteristic
1283C22C47×#53411yescharacteristic
1284C22C47×#53411yescharacteristic
1285C22C47×#53511yescharacteristic
1286C22C47×#53511yescharacteristic
1287C22C47×#53511yescharacteristic
1288C22C47×#53711yescharacteristic
1289C22C47×#53811yescharacteristic
1290C22C47×#53811yescharacteristic
1291C22C47×#53811yescharacteristic
1292C22C47×#53911yescharacteristic
1293C22C47×#54011yescharacteristic
1294C22C47×#54011yescharacteristic
1295C22D42×C4711yescharacteristic
1296C22D42×C4711yescharacteristic
1297C22D42×C4711yescharacteristic
1298C22C47×#54611yescharacteristic
1299C22C47×#54611yescharacteristic
1300C22C47×#54611yescharacteristic
1301C22C47×#54611yescharacteristic
1302C22C47×#54711yescharacteristic
1303C22C47×#54811yescharacteristic
1304C22C47×#55111yescharacteristic
1305C22C47×#55111yescharacteristic
1306C22C47×#55311yescharacteristic
1307C22C47×#56011yescharacteristic
1308C22C47×#56011yescharacteristic
1309C22C47×#56211yescharacteristic
1310C22C47×#56211yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C2—44no—
1324C2—44no—
1325C2—82no—
1326C2C47×#232111yescharacteristic
1327C2C47×#232511yescharacteristic
1328C2C47×#232811yescharacteristic
1329C2C47×#235811yescharacteristic
1330C2C47×#235811yescharacteristic
1331C2C47×#236111yescharacteristic
1332C2C47×#237711yescharacteristic
1333C2C47×#266911yescharacteristic
1334C2C47×#267111yescharacteristic
1335C2C47×#267611yescharacteristic
1336C2C47×#267811yescharacteristic
1337C2C47×#268811yescharacteristic
1338C2C47×#269611yescharacteristic
1339C2C47×#270611yescharacteristic
1340C2C47×#274911yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC2×C47×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#390C2semidirect
3. C2×C47×#386C2semidirect
4. C2×C47×#386C2semidirect
5. C2×C47×#386C2semidirect
6. C2×C47×#386C2semidirect
7. C2×C47×#385C2semidirect
8. C47×#1442C2semidirect
9. C47×#1440C2semidirect
10. C47×#1439C2semidirect
11. C47×#1439C2semidirect
12. C47×#1438C2semidirect
13. C47×#1437C2semidirect
14. C47×#1434C2semidirect
15. C47×C22⋊#95C2semidirect
37. C47×#392C4semidirect
80. C22×D4×C47C2×C4semidirect
81. C22×D4×C47C2×C4semidirect
148. C2×C22⋊C4×C47C2×C4semidirect
149. C2×C22⋊C4×C47C2×C4semidirect
150. C2×C22⋊C4×C47C2×C4semidirect
151. C2×C22⋊C4×C47D4semidirect
152. C2×C22⋊C4×C47D4semidirect
168. #95×C47C2×C4semidirect
169. #95×C47D4semidirect
560. #14519C47direct (N × H)
654. C2×#390C2×C47semidirect
655. C2×#386C2×C47semidirect
656. C2×#386C2×C47semidirect
657. C2×#386C2×C47semidirect
658. C2×#386C2×C47semidirect
659. C2×#385C2×C47semidirect
660. #1442C2×C47semidirect
661. #1440C2×C47semidirect
662. #1439C2×C47semidirect
663. #1439C2×C47semidirect
664. #1438C2×C47semidirect
665. #1437C2×C47semidirect
666. #1434C2×C47semidirect
667. C22⋊#95C2×C47semidirect
707. #392C4×C47semidirect
728. C47#14519direct (N × H)
751. C22×D4C2×C4×C47semidirect
752. C22×D4C2×C4×C47semidirect
819. C2×C22⋊C4C2×C4×C47semidirect
820. C2×C22⋊C4C2×C4×C47semidirect
821. C2×C22⋊C4C2×C4×C47semidirect
822. C2×C22⋊C4D4×C47semidirect
823. C2×C22⋊C4D4×C47semidirect
839. #95C2×C4×C47semidirect
840. #95D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#3922
C2×C47×#3902
C2×C47×#3862
C2×C47×#3852
C47×#14422
C47×#14402
C47×#14392
C47×#14382
C47×#14372
C47×#14342
C47×C22⋊#952
#1451947