Finite Group Databasebeta

← C47×#14520 #26054218

Subgroups — C47×#14520 #26054218

Order 12032.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 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×#388C211yesmaximal, characteristic, complemented
4C2×C47×#386C211yesmaximal, characteristic, complemented
5C2×C47×#386C211yesmaximal, characteristic, complemented
6C47×#1442C211yesmaximal, characteristic, complemented
7C47×#1440C211yesmaximal, characteristic, complemented
8C47×#1438C211yesmaximal, characteristic, complemented
9C47×#1438C211yesmaximal, characteristic, complemented
10C47×#1438C211yesmaximal, characteristic, complemented
11C47×#1437C211yesmaximal, characteristic, complemented
12C47×#1437C211yesmaximal, 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
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
35C22×C42×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C47×#392C418yescomplemented
38C47×#390—24no—
39C47×#388—24no—
40C47×#386—24no—
41C47×#386—24no—
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
55C2×#95×C47C2211yescharacteristic
56C25×C47C2311yescharacteristic
57C25×C47C2311yescharacteristic
58C25×C47C2311yescharacteristic
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—41no—
66C22×D4×C47—41no—
67C22×D4×C47—41no—
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×C47C2×C414yes—
78C22×D4×C47C2×C414yes—
79C22×D4×C47C2×C414yescomplemented
80C23×C4×C47—22no—
81C23×C4×C47—22no—
82C23×C4×C47—22no—
83C23×C4×C47—41no—
84C23×C4×C47—41no—
85C23×C4×C47—41no—
86C23×C4×C47—41no—
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
98C23×C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—41no—
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—22no—
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×C47C2×C414yes—
141C2×C22⋊C4×C47C2×C414yescomplemented
142C2×C22⋊C4×C47C2×C414yescomplemented
143C2×C22⋊C4×C47D414yescomplemented
144C2×C42×C47—22no—
145C2×C42×C47—22no—
146C2×C42×C47—22no—
147C2×C42×C47—41no—
148C2×C42×C47—41no—
149C2×C42×C47—41no—
150#95×C47—22no—
151#95×C47—22no—
152#95×C47—22no—
153#95×C47—22no—
154#95×C47—41no—
155#95×C47—41no—
156#95×C47—41no—
157#95×C47—41no—
158#95×C47—41no—
159#95×C47—41no—
160#95×C47—41no—
161#95×C47—41no—
162#95×C47C2×C414yescomplemented
163#95×C47D414yescomplemented
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×C47—21no—
200C24×C47—21no—
201C24×C47—21no—
202C24×C47—21no—
203C24×C47—21no—
204C24×C47C22×C412yes—
205C24×C47C22×C412yes—
206C24×C47C22×C412yes—
207C24×C47C2×D412yes—
208C24×C47#4112yes—
209C24×C47C2411yescharacteristic
210C2×D4×C47—28no—
211C2×D4×C47—28no—
212C2×D4×C47—28no—
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—
226C2×D4×C47—44no—
227C2×D4×C47—44no—
228C2×D4×C47—44no—
229C2×D4×C47—44no—
230C2×D4×C47—44no—
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—44no—
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×C47C22×C412yes—
311C22×C4×C47C22×C412yes—
312C22×C4×C47C22×C412yes—
313C22×C4×C47C22×C412yes—
314C22×C4×C47C2×D412yes—
315C22×C4×C47C2×D412yes—
316C22×C4×C47C2×D412yes—
317C22×C4×C47C2×D412yes—
318C22×C4×C47C2×D412yes—
319C22×C4×C47#4112yes—
320C22×C4×C47#4112yes—
321C22×C4×C47#4112yes—
322C4⋊C4×C47—44no—
323C22⋊C4×C47—28no—
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—
332C22⋊C4×C47—44no—
333C22⋊C4×C47—44no—
334C22⋊C4×C47—44no—
335C22⋊C4×C47—44no—
336C22⋊C4×C47—44no—
337C42×C47—44no—
338C42×C47—44no—
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—22no—
365C23×C47—22no—
366C23×C47—22no—
367C23×C47—22no—
368C23×C47—22no—
369C23×C47—22no—
370C23×C47—22no—
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—41no—
437C23×C47—41no—
438C23×C47—41no—
439C23×C47—41no—
440C23×C47—41no—
441C23×C47—41no—
442C23×C47—41no—
443C23×C47C4×D414yes—
444C23×C47C23×C411yescharacteristic
445C23×C47C22×D411yescharacteristic
446C23×C47C22×D411yescharacteristic
447C23×C47C2×#4111yescharacteristic
448C23×C47C2×#4111yescharacteristic
449C23×C47C2×#4111yescharacteristic
450C23×C47C2×#4111yescharacteristic
451C23×C47H(5,𝔽2)11yescharacteristic
452C23×C47H(5,𝔽2)11yescharacteristic
453C23×C47H(5,𝔽2)11yescharacteristic
454C23×C47H(5,𝔽2)11yescharacteristic
455C23×C47H(5,𝔽2)11yescharacteristic
456C23×C47H(5,𝔽2)11yescharacteristic
457C23×C47H(5,𝔽2)11yescharacteristic
458C23×C47H(5,𝔽2)11yescharacteristic
459D4×C47—416no—
460D4×C47—416no—
461D4×C47—416no—
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—22no—
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—416no—
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—
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×C47C4×D414yes—
547#14520C4711yesmaximal, characteristic, direct product factor, Sylow
548C22×C47—24no—
549C22×C47—24no—
550C22×C47—24no—
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—42no—
571C22×C47—42no—
572C22×C47—42no—
573C22×C47—42no—
574C22×C47—42no—
575C22×C47—42no—
576C22×C47—42no—
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×C47—81no—
587C22×C47—81no—
588C22×C47—81no—
589C22×C47—81no—
590C22×C47—81no—
591C22×C47—81no—
592C22×C47—81no—
593C22×C47C2×C4×D411yescharacteristic
594C22×C47C2×C4×D411yescharacteristic
595C22×C47C4×#4111yescharacteristic
596C22×C47#51811yescharacteristic
597C22×C47#51811yescharacteristic
598C22×C47#51811yescharacteristic
599C22×C47#51811yescharacteristic
600C22×C47#53411yescharacteristic
601C22×C47#53511yescharacteristic
602C22×C47#53511yescharacteristic
603C22×C47#53511yescharacteristic
604C22×C47#53811yescharacteristic
605C22×C47#53811yescharacteristic
606C22×C47#53811yescharacteristic
607C22×C47#53811yescharacteristic
608C22×C47#54011yescharacteristic
609C22×C47#54011yescharacteristic
610C22×C47#54011yescharacteristic
611C22×C47#54011yescharacteristic
612C22×C47D4211yescharacteristic
613C22×C47#54611yescharacteristic
614C22×C47#54611yescharacteristic
615C22×C47#54611yescharacteristic
616C22×C47#54611yescharacteristic
617C22×C47#54611yescharacteristic
618C22×C47#55011yescharacteristic
619C22×C47#55111yescharacteristic
620C22×C47#55311yescharacteristic
621C22×C47#55311yescharacteristic
622C22×C47#55311yescharacteristic
623C22×C47#55511yescharacteristic
624C22×C47#56011yescharacteristic
625C22×C47#56011yescharacteristic
626C22×C47#56011yescharacteristic
627C22×C47H(3,𝔽4)11yescharacteristic
628C4×C47—24no—
629C4×C47—42no—
630C4×C47—42no—
631C4×C47—42no—
632C4×C47—42no—
633C4×C47—42no—
634C4×C47—42no—
635C4×C47—42no—
636C4×C47—42no—
637C4×C47—42no—
638C4×C47—81no—
639C4×C47—81no—
640C2×#392C2×C4711yescharacteristic
641C2×#390C2×C4711yescharacteristic, complemented
642C2×#388C2×C4711yescharacteristic, complemented
643C2×#386C2×C4711yescharacteristic, complemented
644C2×#386C2×C4711yescharacteristic, complemented
645#1442C2×C4711yescharacteristic, complemented
646#1440C2×C4711yescharacteristic, complemented
647#1438C2×C4711yescharacteristic, complemented
648#1438C2×C4711yescharacteristic, complemented
649#1438C2×C4711yescharacteristic, complemented
650#1437C2×C4711yescharacteristic, complemented
651#1437C2×C4711yescharacteristic, complemented
652#1437C2×C4711yescharacteristic, complemented
653#1434C2×C4711yescharacteristic, complemented
654C22⋊#95C2×C4711yescharacteristic, complemented
655C2×C47—44no—
656C2×C47—82no—
657C2×C47—82no—
658C2×C47#232111yescharacteristic
659C2×C47#232811yescharacteristic
660C2×C47#233311yescharacteristic
661C2×C47#235811yescharacteristic
662C2×C47#236311yescharacteristic
663C2×C47#236411yescharacteristic
664C2×C47#237511yescharacteristic
665C2×C47#267011yescharacteristic
666C2×C47#267311yescharacteristic
667C2×C47#269911yescharacteristic
668C2×C47#270311yescharacteristic
669C2×C47#270311yescharacteristic
670C2×C47#271411yescharacteristic
671C2×C47#275311yescharacteristic
672C2×C47#275611yescharacteristic
673C23×D4C22×C4711yescharacteristic
674C23×D4C22×C4711yescharacteristic
675C23×D4C22×C4711yescharacteristic
676C24×C4C22×C4711yescharacteristic
677C22×C4⋊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
685C22×C22⋊C4C22×C4711yescharacteristic
686C22×C22⋊C4C22×C4711yescharacteristic
687C22×C22⋊C4C22×C4711yescharacteristic
688C22×C22⋊C4C22×C4711yescharacteristic
689C22×C22⋊C4C22×C4711yescharacteristic
690C22×C22⋊C4C22×C4711yescharacteristic
691C22×C22⋊C4C22×C4711yescharacteristic
692C22×C42C22×C4711yescharacteristic
693C22×C42C22×C4711yescharacteristic
694#392C4×C4718yescomplemented
695#390—24no—
696#388—24no—
697#386—24no—
698#386—24no—
699C2×#95C22×C4711yescharacteristic
700C2×#95C22×C4711yescharacteristic
701C2×#95C22×C4711yescharacteristic
702C2×#95C22×C4711yescharacteristic
703C2×#95C22×C4711yescharacteristic
704C2×#95C22×C4711yescharacteristic
705C2×#95C22×C4711yescharacteristic
706C2×#95C22×C4711yescharacteristic
707C2×#95C22×C4711yescharacteristic
708C2×#95C22×C4711yescharacteristic
709C2×#95C22×C4711yescharacteristic
710C2×#95C22×C4711yescharacteristic
711C2×#95C22×C4711yescharacteristic
712C2×#95C22×C4711yescharacteristic
713C47#1452011yescharacteristic, direct product factor, Sylow
714C25C23×C4711yescharacteristic
715C25C23×C4711yescharacteristic
716C25C23×C4711yescharacteristic
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4C2×C4×C4714yes—
736C22×D4C2×C4×C4714yes—
737C22×D4C2×C4×C4714yescomplemented
738C23×C4—22no—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—41no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4C23×C4711yescharacteristic
746C23×C4C23×C4711yescharacteristic
747C23×C4C23×C4711yescharacteristic
748C23×C4C23×C4711yescharacteristic
749C23×C4C23×C4711yescharacteristic
750C23×C4C23×C4711yescharacteristic
751C23×C4C23×C4711yescharacteristic
752C23×C4C23×C4711yescharacteristic
753C23×C4C23×C4711yescharacteristic
754C23×C4C23×C4711yescharacteristic
755C23×C4C23×C4711yescharacteristic
756C23×C4C23×C4711yescharacteristic
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—41no—
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—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
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—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4C2×C4×C4714yes—
799C2×C22⋊C4C2×C4×C4714yescomplemented
800C2×C22⋊C4C2×C4×C4714yescomplemented
801C2×C22⋊C4D4×C4714yescomplemented
802C2×C42—22no—
803C2×C42—22no—
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807C2×C42—41no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—41no—
813#95—41no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95—41no—
819#95—41no—
820#95C2×C4×C4714yescomplemented
821#95D4×C4714yescomplemented
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—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24C22×C4×C4712yes—
863C24C22×C4×C4712yes—
864C24C22×C4×C4712yes—
865C24C2×D4×C4712yes—
866C24#41×C4712yes—
867C24C24×C4711yescharacteristic
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
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—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4C22×C4×C4712yes—
969C22×C4C22×C4×C4712yes—
970C22×C4C22×C4×C4712yes—
971C22×C4C22×C4×C4712yes—
972C22×C4C2×D4×C4712yes—
973C22×C4C2×D4×C4712yes—
974C22×C4C2×D4×C4712yes—
975C22×C4C2×D4×C4712yes—
976C22×C4C2×D4×C4712yes—
977C22×C4#41×C4712yes—
978C22×C4#41×C4712yes—
979C22×C4#41×C4712yes—
980C4⋊C4—44no—
981C22⋊C4—28no—
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⋊C4—44no—
995C42—44no—
996C42—44no—
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—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
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—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—
1101C23C4×D4×C4714yes—
1102C23C23×C4×C4711yescharacteristic
1103C23C22×D4×C4711yescharacteristic
1104C23C22×D4×C4711yescharacteristic
1105C23C2×#41×C4711yescharacteristic
1106C23C2×#41×C4711yescharacteristic
1107C23C2×#41×C4711yescharacteristic
1108C23C2×#41×C4711yescharacteristic
1109C23H(5,𝔽2)×C4711yescharacteristic
1110C23H(5,𝔽2)×C4711yescharacteristic
1111C23H(5,𝔽2)×C4711yescharacteristic
1112C23H(5,𝔽2)×C4711yescharacteristic
1113C23H(5,𝔽2)×C4711yescharacteristic
1114C23H(5,𝔽2)×C4711yescharacteristic
1115C23H(5,𝔽2)×C4711yescharacteristic
1116C23H(5,𝔽2)×C4711yescharacteristic
1117D4—416no—
1118D4—416no—
1119D4—416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
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—416no—
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—
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×C4C4×D4×C4714yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
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—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×C4×D4×C4711yescharacteristic
1251C22C2×C4×D4×C4711yescharacteristic
1252C22C4×#41×C4711yescharacteristic
1253C22C47×#51811yescharacteristic
1254C22C47×#51811yescharacteristic
1255C22C47×#51811yescharacteristic
1256C22C47×#51811yescharacteristic
1257C22C47×#53411yescharacteristic
1258C22C47×#53511yescharacteristic
1259C22C47×#53511yescharacteristic
1260C22C47×#53511yescharacteristic
1261C22C47×#53811yescharacteristic
1262C22C47×#53811yescharacteristic
1263C22C47×#53811yescharacteristic
1264C22C47×#53811yescharacteristic
1265C22C47×#54011yescharacteristic
1266C22C47×#54011yescharacteristic
1267C22C47×#54011yescharacteristic
1268C22C47×#54011yescharacteristic
1269C22D42×C4711yescharacteristic
1270C22C47×#54611yescharacteristic
1271C22C47×#54611yescharacteristic
1272C22C47×#54611yescharacteristic
1273C22C47×#54611yescharacteristic
1274C22C47×#54611yescharacteristic
1275C22C47×#55011yescharacteristic
1276C22C47×#55111yescharacteristic
1277C22C47×#55311yescharacteristic
1278C22C47×#55311yescharacteristic
1279C22C47×#55311yescharacteristic
1280C22C47×#55511yescharacteristic
1281C22C47×#56011yescharacteristic
1282C22C47×#56011yescharacteristic
1283C22C47×#56011yescharacteristic
1284C22C47×H(3,𝔽4)11yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2C47×#232111yescharacteristic
1301C2C47×#232811yescharacteristic
1302C2C47×#233311yescharacteristic
1303C2C47×#235811yescharacteristic
1304C2C47×#236311yescharacteristic
1305C2C47×#236411yescharacteristic
1306C2C47×#237511yescharacteristic
1307C2C47×#267011yescharacteristic
1308C2C47×#267311yescharacteristic
1309C2C47×#269911yescharacteristic
1310C2C47×#270311yescharacteristic
1311C2C47×#270311yescharacteristic
1312C2C47×#271411yescharacteristic
1313C2C47×#275311yescharacteristic
1314C2C47×#275611yescharacteristic
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×#388C2semidirect
4. C2×C47×#386C2semidirect
5. C2×C47×#386C2semidirect
6. C47×#1442C2semidirect
7. C47×#1440C2semidirect
8. C47×#1438C2semidirect
9. C47×#1438C2semidirect
10. C47×#1438C2semidirect
11. C47×#1437C2semidirect
12. C47×#1437C2semidirect
13. C47×#1437C2semidirect
14. C47×#1434C2semidirect
15. C47×C22⋊#95C2semidirect
37. C47×#392C4semidirect
79. C22×D4×C47C2×C4semidirect
141. C2×C22⋊C4×C47C2×C4semidirect
142. C2×C22⋊C4×C47C2×C4semidirect
143. C2×C22⋊C4×C47D4semidirect
162. #95×C47C2×C4semidirect
163. #95×C47D4semidirect
547. #14520C47direct (N × H)
641. C2×#390C2×C47semidirect
642. C2×#388C2×C47semidirect
643. C2×#386C2×C47semidirect
644. C2×#386C2×C47semidirect
645. #1442C2×C47semidirect
646. #1440C2×C47semidirect
647. #1438C2×C47semidirect
648. #1438C2×C47semidirect
649. #1438C2×C47semidirect
650. #1437C2×C47semidirect
651. #1437C2×C47semidirect
652. #1437C2×C47semidirect
653. #1434C2×C47semidirect
654. C22⋊#95C2×C47semidirect
694. #392C4×C47semidirect
713. C47#14520direct (N × H)
737. C22×D4C2×C4×C47semidirect
799. C2×C22⋊C4C2×C4×C47semidirect
800. C2×C22⋊C4C2×C4×C47semidirect
801. C2×C22⋊C4D4×C47semidirect
820. #95C2×C4×C47semidirect
821. #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×#3882
C2×C47×#3862
C47×#14422
C47×#14402
C47×#14382
C47×#14372
C47×#14342
C47×C22⋊#952
#1452047