Finite Group Databasebeta

← C47×#16287 #26055985

Subgroups — C47×#16287 #26055985

Order 12032.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#397C211yesmaximal, characteristic, complemented
2C2×C47×#394C211yesmaximal, characteristic, complemented
3C2×C47×#394C211yesmaximal, characteristic, complemented
4C2×C47×#392C211yesmaximal, characteristic
5C2×C47×#386C211yesmaximal, characteristic, complemented
6C2×C47×#386C211yesmaximal, characteristic, complemented
7C47×#1442C211yesmaximal, characteristic, complemented
8C47×#1442C211yesmaximal, characteristic, complemented
9C47×#1439C211yesmaximal, characteristic, complemented
10C47×#1439C211yesmaximal, characteristic, complemented
11C47×#1439C211yesmaximal, characteristic, complemented
12C47×#1439C211yesmaximal, 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×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×C22⋊C4×C47C2211yescharacteristic
37C47×#397—24no—
38C47×#394—24no—
39C47×#394—24no—
40C47×#392—24no—
41C47×#386—24no—
42C47×#386—24no—
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
56C2×#95×C47C2211yescharacteristic
57C25×C47C2311yescharacteristic
58C25×C47C2311yescharacteristic
59C25×C47C2311yescharacteristic
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—22no—
69C22×D4×C47—22no—
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×C47—41no—
79C22×D4×C47—41no—
80C22×D4×C47D414yes—
81C23×C4×C47—22no—
82C23×C4×C47—22no—
83C23×C4×C47—22no—
84C23×C4×C47—41no—
85C23×C4×C47—41no—
86C23×C4×C47—41no—
87C23×C4×C47—41no—
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
99C23×C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—41no—
104C2×C4⋊C4×C47—41no—
105C2×C4⋊C4×C47—41no—
106C2×C4⋊C4×C47—41no—
107C2×C4⋊C4×C47—41no—
108C2×C4⋊C4×C47—41no—
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—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—22no—
131C2×C22⋊C4×C47—22no—
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×C47—41no—
149C2×C22⋊C4×C47—41no—
150C2×C22⋊C4×C47D414yescomplemented
151#95×C47—22no—
152#95×C47—22no—
153#95×C47—22no—
154#95×C47—22no—
155#95×C47—22no—
156#95×C47—22no—
157#95×C47—22no—
158#95×C47—22no—
159#95×C47—22no—
160#95×C47—41no—
161#95×C47—41no—
162#95×C47—41no—
163#95×C47—41no—
164#95×C47D414yescomplemented
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×C47—21no—
205C24×C47C2×D412yes—
206C24×C47C2×D412yes—
207C24×C47C2×D412yes—
208C24×C47#4112yes—
209C24×C47#4112yes—
210C24×C47C2411yescharacteristic
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—
231C2×D4×C47—44no—
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—21no—
305C22×C4×C47—21no—
306C22×C4×C47—21no—
307C22×C4×C47—21no—
308C22×C4×C47—44no—
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×C47C2×D412yes—
316C22×C4×C47C2×D412yes—
317C22×C4×C47C2×D412yes—
318C22×C4×C47C2×D412yes—
319C22×C4×C47C2×D412yes—
320C22×C4×C47C2×D412yes—
321C22×C4×C47#4112yes—
322C22×C4×C47#4112yes—
323C4⋊C4×C47—44no—
324C4⋊C4×C47—44no—
325C4⋊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—
337C22⋊C4×C47—44no—
338C22⋊C4×C47—44no—
339C22⋊C4×C47—44no—
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—22no—
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×C47—41no—
444C23×C47#12114yes—
445C23×C47C22×D411yescharacteristic
446C23×C47C22×D411yescharacteristic
447C23×C47C22×D411yescharacteristic
448C23×C47C2×#4111yescharacteristic
449C23×C47C2×#4111yescharacteristic
450C23×C47C2×#4111yescharacteristic
451C23×C47C2×#4111yescharacteristic
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
459C23×C472−1+411yescharacteristic
460D4×C47—416no—
461D4×C47—416no—
462D4×C47—416no—
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—416no—
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—
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—
548#16287C4711yesmaximal, characteristic, direct product factor, Sylow
549C22×C47—24no—
550C22×C47—24no—
551C22×C47—24no—
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—42no—
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×C47—81no—
594C22×C47C2×#12111yescharacteristic
595C22×C47#52511yescharacteristic
596C22×C47#52911yescharacteristic
597C22×C47#53411yescharacteristic
598C22×C47#53411yescharacteristic
599C22×C47#53411yescharacteristic
600C22×C47#53511yescharacteristic
601C22×C47#53511yescharacteristic
602C22×C47#53711yescharacteristic
603C22×C47#53811yescharacteristic
604C22×C47#53811yescharacteristic
605C22×C47#53811yescharacteristic
606C22×C47#53811yescharacteristic
607C22×C47#53811yescharacteristic
608C22×C47#53811yescharacteristic
609C22×C47#53911yescharacteristic
610C22×C47#53911yescharacteristic
611C22×C47#54011yescharacteristic
612C22×C47#54011yescharacteristic
613C22×C47D4211yescharacteristic
614C22×C47D4211yescharacteristic
615C22×C47#54611yescharacteristic
616C22×C47#54611yescharacteristic
617C22×C47#54611yescharacteristic
618C22×C47#54611yescharacteristic
619C22×C47#54611yescharacteristic
620C22×C47#54711yescharacteristic
621C22×C47#54711yescharacteristic
622C22×C47#55011yescharacteristic
623C22×C47#55111yescharacteristic
624C22×C47#55311yescharacteristic
625C22×C47#56011yescharacteristic
626C22×C47H(3,𝔽4)11yescharacteristic
627C22×C47#56211yescharacteristic
628C22×C47#56211yescharacteristic
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—81no—
638C4×C47—81no—
639C4×C47—81no—
640C4×C47—81no—
641C2×#397C2×C4711yescharacteristic, complemented
642C2×#394C2×C4711yescharacteristic, complemented
643C2×#394C2×C4711yescharacteristic, complemented
644C2×#392C2×C4711yescharacteristic
645C2×#386C2×C4711yescharacteristic, complemented
646C2×#386C2×C4711yescharacteristic, complemented
647#1442C2×C4711yescharacteristic, complemented
648#1442C2×C4711yescharacteristic, complemented
649#1439C2×C4711yescharacteristic, complemented
650#1439C2×C4711yescharacteristic, complemented
651#1439C2×C4711yescharacteristic, complemented
652#1439C2×C4711yescharacteristic, complemented
653#1438C2×C4711yescharacteristic, complemented
654#1438C2×C4711yescharacteristic, complemented
655C22⋊#95C2×C4711yescharacteristic, complemented
656C2×C47—44no—
657C2×C47—82no—
658C2×C47—82no—
659C2×C47#242411yescharacteristic
660C2×C47#242511yescharacteristic
661C2×C47#246711yescharacteristic
662C2×C47#261711yescharacteristic
663C2×C47#263611yescharacteristic
664C2×C47#264811yescharacteristic
665C2×C47#267011yescharacteristic
666C2×C47#267111yescharacteristic
667C2×C47#267311yescharacteristic
668C2×C47#268211yescharacteristic
669C2×C47#268411yescharacteristic
670C2×C47#268811yescharacteristic
671C2×C47#270611yescharacteristic
672C2×C47#270811yescharacteristic
673C2×C47#282411yescharacteristic
674C23×D4C22×C4711yescharacteristic
675C23×D4C22×C4711yescharacteristic
676C23×D4C22×C4711yescharacteristic
677C24×C4C22×C4711yescharacteristic
678C22×C4⋊C4C22×C4711yescharacteristic
679C22×C4⋊C4C22×C4711yescharacteristic
680C22×C4⋊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×C22⋊C4C22×C4711yescharacteristic
693C22×C22⋊C4C22×C4711yescharacteristic
694C22×C22⋊C4C22×C4711yescharacteristic
695#397—24no—
696#394—24no—
697#394—24no—
698#392—24no—
699#386—24no—
700#386—24no—
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
713C2×#95C22×C4711yescharacteristic
714C2×#95C22×C4711yescharacteristic
715C47#1628711yescharacteristic, direct product factor, Sylow
716C25C23×C4711yescharacteristic
717C25C23×C4711yescharacteristic
718C25C23×C4711yescharacteristic
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4D4×C4714yes—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—22no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4—41no—
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
757C23×C4C23×C4711yescharacteristic
758C23×C4C23×C4711yescharacteristic
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—41no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C4⋊C4—41no—
766C2×C4⋊C4—41no—
767C2×C4⋊C4—41no—
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—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
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—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⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
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⋊C4D4×C4714yescomplemented
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95—41no—
823#95D4×C4714yescomplemented
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—
862C24—21no—
863C24—21no—
864C24C2×D4×C4712yes—
865C24C2×D4×C4712yes—
866C24C2×D4×C4712yes—
867C24#41×C4712yes—
868C24#41×C4712yes—
869C24C24×C4711yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
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—
889C2×D4—44no—
890C2×D4—44no—
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—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4C2×D4×C4712yes—
975C22×C4C2×D4×C4712yes—
976C22×C4C2×D4×C4712yes—
977C22×C4C2×D4×C4712yes—
978C22×C4C2×D4×C4712yes—
979C22×C4C2×D4×C4712yes—
980C22×C4#41×C4712yes—
981C22×C4#41×C4712yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊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—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
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—22no—
1030C23—22no—
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—
1101C23—41no—
1102C23—41no—
1103C23#121×C4714yes—
1104C23C22×D4×C4711yescharacteristic
1105C23C22×D4×C4711yescharacteristic
1106C23C22×D4×C4711yescharacteristic
1107C23C2×#41×C4711yescharacteristic
1108C23C2×#41×C4711yescharacteristic
1109C23C2×#41×C4711yescharacteristic
1110C23C2×#41×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
1117C23H(5,𝔽2)×C4711yescharacteristic
1118C232−1+4×C4711yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
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—416no—
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—
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—
1207C22—24no—
1208C22—24no—
1209C22—24no—
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—42no—
1235C22—42no—
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—
1250C22—81no—
1251C22—81no—
1252C22C2×#121×C4711yescharacteristic
1253C22C47×#52511yescharacteristic
1254C22C47×#52911yescharacteristic
1255C22C47×#53411yescharacteristic
1256C22C47×#53411yescharacteristic
1257C22C47×#53411yescharacteristic
1258C22C47×#53511yescharacteristic
1259C22C47×#53511yescharacteristic
1260C22C47×#53711yescharacteristic
1261C22C47×#53811yescharacteristic
1262C22C47×#53811yescharacteristic
1263C22C47×#53811yescharacteristic
1264C22C47×#53811yescharacteristic
1265C22C47×#53811yescharacteristic
1266C22C47×#53811yescharacteristic
1267C22C47×#53911yescharacteristic
1268C22C47×#53911yescharacteristic
1269C22C47×#54011yescharacteristic
1270C22C47×#54011yescharacteristic
1271C22D42×C4711yescharacteristic
1272C22D42×C4711yescharacteristic
1273C22C47×#54611yescharacteristic
1274C22C47×#54611yescharacteristic
1275C22C47×#54611yescharacteristic
1276C22C47×#54611yescharacteristic
1277C22C47×#54611yescharacteristic
1278C22C47×#54711yescharacteristic
1279C22C47×#54711yescharacteristic
1280C22C47×#55011yescharacteristic
1281C22C47×#55111yescharacteristic
1282C22C47×#55311yescharacteristic
1283C22C47×#56011yescharacteristic
1284C22C47×H(3,𝔽4)11yescharacteristic
1285C22C47×#56211yescharacteristic
1286C22C47×#56211yescharacteristic
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C47×#242411yescharacteristic
1303C2C47×#242511yescharacteristic
1304C2C47×#246711yescharacteristic
1305C2C47×#261711yescharacteristic
1306C2C47×#263611yescharacteristic
1307C2C47×#264811yescharacteristic
1308C2C47×#267011yescharacteristic
1309C2C47×#267111yescharacteristic
1310C2C47×#267311yescharacteristic
1311C2C47×#268211yescharacteristic
1312C2C47×#268411yescharacteristic
1313C2C47×#268811yescharacteristic
1314C2C47×#270611yescharacteristic
1315C2C47×#270811yescharacteristic
1316C2C47×#282411yescharacteristic
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
2. C2×C47×#394C2semidirect
3. C2×C47×#394C2semidirect
5. C2×C47×#386C2semidirect
6. C2×C47×#386C2semidirect
7. C47×#1442C2semidirect
8. C47×#1442C2semidirect
9. C47×#1439C2semidirect
10. C47×#1439C2semidirect
11. C47×#1439C2semidirect
12. C47×#1439C2semidirect
13. C47×#1438C2semidirect
14. C47×#1438C2semidirect
15. C47×C22⋊#95C2semidirect
150. C2×C22⋊C4×C47D4semidirect
164. #95×C47D4semidirect
548. #16287C47direct (N × H)
641. C2×#397C2×C47semidirect
642. C2×#394C2×C47semidirect
643. C2×#394C2×C47semidirect
645. C2×#386C2×C47semidirect
646. C2×#386C2×C47semidirect
647. #1442C2×C47semidirect
648. #1442C2×C47semidirect
649. #1439C2×C47semidirect
650. #1439C2×C47semidirect
651. #1439C2×C47semidirect
652. #1439C2×C47semidirect
653. #1438C2×C47semidirect
654. #1438C2×C47semidirect
655. C22⋊#95C2×C47semidirect
715. C47#16287direct (N × H)
809. C2×C22⋊C4D4×C47semidirect
823. #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×#3942
C2×C47×#3922
C2×C47×#3862
C47×#14422
C47×#14392
C47×#14382
C47×C22⋊#952
#1628747