Finite Group Databasebeta

← C47×#13873 #26053571

Subgroups — C47×#13873 #26053571

Order 12032.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C47C211yesmaximal, characteristic
2C2×C47×#388C212yesmaximal, complemented
3C2×C47×#380C211yesmaximal, characteristic, complemented
4C2×C47×#379C211yesmaximal, characteristic
5C2×C47×#379C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
7C47×#1440C212yesmaximal, complemented
8C47×#1439C212yesmaximal, complemented
9C47×#1437C212yesmaximal, complemented
10C47×C22⋊#95C211yesmaximal, characteristic, complemented
11C47×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C47C2211yescharacteristic
13C24×C4×C47C2211yescharacteristic
14C24×C4×C47C2211yescharacteristic
15C22×C4⋊C4×C47C2212yescomplemented
16C22×C22⋊C4×C47—28no—
17C22×C22⋊C4×C47C418yescomplemented
18C22×C22⋊C4×C47C2211yescharacteristic
19C22×C22⋊C4×C47C2211yescharacteristic
20C22×C22⋊C4×C47C2212yes—
21C22×C22⋊C4×C47C2212yes—
22C22×C22⋊C4×C47C2212yes—
23C22×C22⋊C4×C47C2212yes—
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×C42×C47C2212yescomplemented
31C47×#388—28no—
32C47×#380—24no—
33C47×#379—24no—
34C47×#379—24no—
35C4×C22⋊C4×C47—24no—
36C2×#95×C47C2212yescomplemented
37C2×#95×C47C2212yescomplemented
38C2×#95×C47C2212yescomplemented
39C2×#95×C47C2212yescomplemented
40C2×#95×C47C2212yescomplemented
41C2×#95×C47C2212yescomplemented
42C25×C47—24no—
43C25×C47—24no—
44C25×C47—22no—
45C25×C47—22no—
46C25×C47—22no—
47C25×C47—22no—
48C25×C47—22no—
49C25×C47—22no—
50C25×C47—42no—
51C25×C47—42no—
52C25×C47C2×C414yes—
53C25×C47C2311yescharacteristic
54C25×C47C2311yescharacteristic
55C25×C47C2311yescharacteristic
56C23×C4×C47—22no—
57C23×C4×C47—22no—
58C23×C4×C47—22no—
59C23×C4×C47—22no—
60C23×C4×C47—24no—
61C23×C4×C47—24no—
62C23×C4×C47—42no—
63C23×C4×C47—42no—
64C23×C4×C47C2×C414yes—
65C23×C4×C47C2×C414yes—
66C23×C4×C47C2312yes—
67C23×C4×C47C2312yes—
68C23×C4×C47C2311yescharacteristic
69C23×C4×C47C2311yescharacteristic
70C23×C4×C47C2312yes—
71C23×C4×C47C2312yes—
72C23×C4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C2×C4⋊C4×C47—24no—
75C2×C4⋊C4×C47—24no—
76C2×C4⋊C4×C47—42no—
77C2×C22⋊C4×C47—24no—
78C2×C22⋊C4×C47—22no—
79C2×C22⋊C4×C47—22no—
80C2×C22⋊C4×C47—22no—
81C2×C22⋊C4×C47—22no—
82C2×C22⋊C4×C47—24no—
83C2×C22⋊C4×C47—24no—
84C2×C22⋊C4×C47—232no—
85C2×C22⋊C4×C47—22no—
86C2×C22⋊C4×C47—22no—
87C2×C22⋊C4×C47—22no—
88C2×C22⋊C4×C47—24no—
89C2×C22⋊C4×C47—24no—
90C2×C22⋊C4×C47—24no—
91C2×C22⋊C4×C47—24no—
92C2×C22⋊C4×C47—22no—
93C2×C22⋊C4×C47—22no—
94C2×C22⋊C4×C47—22no—
95C2×C22⋊C4×C47—24no—
96C2×C22⋊C4×C47—24no—
97C2×C22⋊C4×C47—24no—
98C2×C22⋊C4×C47—24no—
99C2×C22⋊C4×C47—42no—
100C2×C22⋊C4×C47—42no—
101C2×C22⋊C4×C47—42no—
102C2×C22⋊C4×C47—42no—
103C2×C22⋊C4×C47C2×C414yes—
104C2×C22⋊C4×C47C2×C414yes—
105C2×C22⋊C4×C47C2×C414yes—
106C2×C22⋊C4×C47C2×C414yes—
107C2×C22⋊C4×C47D414yes—
108C2×C22⋊C4×C47D414yes—
109C2×C22⋊C4×C47D418yes—
110C2×C42×C47—24no—
111C2×C42×C47—24no—
112C2×C42×C47—42no—
113#95×C47—24no—
114#95×C47—24no—
115#95×C47—24no—
116#95×C47—24no—
117#95×C47—42no—
118#95×C47—42no—
119C24×C47—22no—
120C24×C47—22no—
121C24×C47—22no—
122C24×C47—22no—
123C24×C47—216no—
124C24×C47—216no—
125C24×C47—28no—
126C24×C47—28no—
127C24×C47—28no—
128C24×C47—22no—
129C24×C47—21no—
130C24×C47—21no—
131C24×C47—21no—
132C24×C47—21no—
133C24×C47—21no—
134C24×C47—21no—
135C24×C47—22no—
136C24×C47—21no—
137C24×C47—21no—
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—21no—
141C24×C47—21no—
142C24×C47—22no—
143C24×C47—22no—
144C24×C47—22no—
145C24×C47—22no—
146C24×C47—28no—
147C24×C47—28no—
148C24×C47—44no—
149C24×C47—44no—
150C24×C47—48no—
151C24×C47—48no—
152C24×C47—48no—
153C24×C47—48no—
154C24×C47—48no—
155C24×C47—48no—
156C24×C47—48no—
157C24×C47—48no—
158C24×C47—48no—
159C24×C47—48no—
160C24×C47—44no—
161C24×C47—44no—
162C24×C47—44no—
163C24×C47—44no—
164C24×C47C22×C412yes—
165C24×C47C22×C412yes—
166C24×C47C22×C412yes—
167C24×C47C2×D414yes—
168C24×C47C2×D412yes—
169C24×C47C2×D412yes—
170C24×C47#4114yes—
171C24×C47#4112yes—
172C24×C47#4112yes—
173C24×C47#4112yes—
174C24×C47#4112yes—
175C24×C47C2411yescharacteristic
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—28no—
183C22×C4×C47—28no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—28no—
205C22×C4×C47—28no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—44no—
221C22×C4×C47—44no—
222C22×C4×C47—48no—
223C22×C4×C47—48no—
224C22×C4×C47—48no—
225C22×C4×C47—48no—
226C22×C4×C47C22×C412yes—
227C22×C4×C47C22×C412yes—
228C22×C4×C47C22×C412yes—
229C22×C4×C47C22×C412yes—
230C22×C4×C47C2×D414yes—
231C22×C4×C47C2×D414yes—
232C22×C4×C47C2×D414yes—
233C22×C4×C47C2×D414yes—
234C4⋊C4×C47—48no—
235C22⋊C4×C47—28no—
236C22⋊C4×C47—28no—
237C22⋊C4×C47—28no—
238C22⋊C4×C47—28no—
239C22⋊C4×C47—28no—
240C22⋊C4×C47—48no—
241C22⋊C4×C47—48no—
242C22⋊C4×C47—48no—
243C22⋊C4×C47—48no—
244C22⋊C4×C47—44no—
245C22⋊C4×C47—44no—
246C22⋊C4×C47C22⋊C4116yescomplemented
247C42×C47—48no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—24no—
253C23×C47—24no—
254C23×C47—24no—
255C23×C47—24no—
256C23×C47—24no—
257C23×C47—24no—
258C23×C47—24no—
259C23×C47—24no—
260C23×C47—24no—
261C23×C47—24no—
262C23×C47—24no—
263C23×C47—24no—
264C23×C47—232no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—24no—
278C23×C47—24no—
279C23×C47—24no—
280C23×C47—24no—
281C23×C47—24no—
282C23×C47—24no—
283C23×C47—24no—
284C23×C47—24no—
285C23×C47—24no—
286C23×C47—24no—
287C23×C47—24no—
288C23×C47—24no—
289C23×C47—416no—
290C23×C47—416no—
291C23×C47—416no—
292C23×C47—416no—
293C23×C47—416no—
294C23×C47—432no—
295C23×C47—432no—
296C23×C47—432no—
297C23×C47—432no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—42no—
307C23×C47—42no—
308C23×C47—42no—
309C23×C47—42no—
310C23×C47—42no—
311C23×C47—42no—
312C23×C47—42no—
313C23×C47—42no—
314C23×C47—42no—
315C23×C47—42no—
316C23×C47—42no—
317C23×C47—42no—
318C23×C47—416no—
319C23×C47C2×C22⋊C414yes—
320C23×C47#11714yes—
321C23×C47#11714yes—
322C23×C47C4×D414yes—
323C23×C47C4×D414yes—
324C23×C47#12114yes—
325C23×C47#12314yes—
326C23×C47#12414yes—
327C23×C47#12614yes—
328C23×C47C23×C411yescharacteristic
329C23×C47C22×D412yes—
330C23×C47C22×D411yescharacteristic
331C23×C47C22×D411yescharacteristic
332C23×C47C2×#4111yescharacteristic
333C23×C47C2×#4111yescharacteristic
334C23×C47C2×#4112yes—
335C23×C47C2×#4111yescharacteristic
336C23×C47C2×#4111yescharacteristic
337C23×C47H(5,𝔽2)12yes—
338C23×C47H(5,𝔽2)12yes—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—24no—
344C2×C4×C47—24no—
345C2×C4×C47—24no—
346C2×C4×C47—24no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—24no—
354C2×C4×C47—24no—
355C2×C4×C47—24no—
356C2×C4×C47—24no—
357C2×C4×C47—24no—
358C2×C4×C47—24no—
359C2×C4×C47—416no—
360C2×C4×C47—416no—
361C2×C4×C47—42no—
362C2×C4×C47—42no—
363C2×C4×C47—42no—
364C2×C4×C47—42no—
365C2×C4×C47—42no—
366C2×C4×C47—42no—
367C2×C4×C47—42no—
368C2×C4×C47—42no—
369C2×C4×C47—42no—
370C2×C4×C47—42no—
371C2×C4×C47—42no—
372C2×C4×C47—42no—
373C2×C4×C47—42no—
374C2×C4×C47—42no—
375C2×C4×C47—42no—
376C2×C4×C47—42no—
377C2×C4×C47—42no—
378C2×C4×C47—42no—
379C2×C4×C47—42no—
380C2×C4×C47—42no—
381C2×C4×C47—42no—
382C2×C4×C47—42no—
383C2×C4×C47—42no—
384C2×C4×C47—42no—
385C2×C4×C47—42no—
386C2×C4×C47—42no—
387C2×C4×C47C2×C22⋊C414yes—
388C2×C4×C47C2×C22⋊C414yes—
389#13873C4711yesmaximal, characteristic, direct product factor, Sylow
390C22×C47—24no—
391C22×C47—24no—
392C22×C47—24no—
393C22×C47—24no—
394C22×C47—24no—
395C22×C47—28no—
396C22×C47—28no—
397C22×C47—28no—
398C22×C47—28no—
399C22×C47—24no—
400C22×C47—24no—
401C22×C47—24no—
402C22×C47—24no—
403C22×C47—24no—
404C22×C47—24no—
405C22×C47—24no—
406C22×C47—464no—
407C22×C47—42no—
408C22×C47—42no—
409C22×C47—42no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47—42no—
413C22×C47—44no—
414C22×C47—44no—
415C22×C47—44no—
416C22×C47—44no—
417C22×C47—44no—
418C22×C47—44no—
419C22×C47—44no—
420C22×C47—44no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47#38818yescomplemented
424C22×C47C22×C22⋊C411yescharacteristic
425C22×C47C2×#11711yescharacteristic
426C22×C47C2×#11711yescharacteristic
427C22×C47C2×C4×D411yescharacteristic
428C22×C47C2×C4×D411yescharacteristic
429C22×C47#51811yescharacteristic
430C22×C47#51811yescharacteristic
431C22×C47C2×#12111yescharacteristic
432C22×C47C2×#12311yescharacteristic
433C22×C47#52512yes—
434C22×C47#52512yes—
435C22×C47C2×#12411yescharacteristic
436C22×C47C2×#12611yescharacteristic
437C22×C47#53812yes—
438C22×C47#53812yes—
439C22×C47D4212yes—
440C22×C47D4212yes—
441C22×C47#54612yes—
442C22×C47#54612yes—
443C22×C47#54612yes—
444C22×C47#54612yes—
445C22×C47#55112yes—
446C22×C47#55112yes—
447C4×C47—24no—
448C4×C47—24no—
449C4×C47—42no—
450C4×C47—42no—
451C4×C47—44no—
452C4×C47—44no—
453C4×C47—82no—
454C4×C47—82no—
455C23×C22⋊C4C2×C4711yescharacteristic
456C2×#388C2×C4712yescomplemented
457C2×#380C2×C4711yescharacteristic, complemented
458C2×#379C2×C4711yescharacteristic
459C2×#379C2×C4711yescharacteristic
460C2×C4×C22⋊C4C2×C4711yescharacteristic, complemented
461#1440C2×C4712yescomplemented
462#1439C2×C4712yescomplemented
463#1437C2×C4712yescomplemented
464C22⋊#95C2×C4711yescharacteristic, complemented
465C22⋊#95C2×C4711yescharacteristic, complemented
466C2×C47—28no—
467C2×C47—44no—
468C2×C47—44no—
469C2×C47#228011yescharacteristic
470C2×C47C2×#38811yescharacteristic
471C2×C47#231211yescharacteristic
472C2×C47D4×C22⋊C411yescharacteristic
473C2×C47D4×C22⋊C411yescharacteristic
474C2×C47#234211yescharacteristic
475C2×C47#234211yescharacteristic
476C2×C47#241812yes—
477C2×C47#242412yes—
478C2×C47#247212yes—
479C2×C47#248012yes—
480C26C22×C4711yescharacteristic
481C24×C4C22×C4711yescharacteristic
482C24×C4C22×C4711yescharacteristic
483C22×C4⋊C4C22×C4712yescomplemented
484C22×C22⋊C4—28no—
485C22×C22⋊C4C4×C4718yescomplemented
486C22×C22⋊C4C22×C4711yescharacteristic
487C22×C22⋊C4C22×C4711yescharacteristic
488C22×C22⋊C4C22×C4712yes—
489C22×C22⋊C4C22×C4712yes—
490C22×C22⋊C4C22×C4712yes—
491C22×C22⋊C4C22×C4712yes—
492C22×C22⋊C4C22×C4711yescharacteristic
493C22×C22⋊C4C22×C4711yescharacteristic
494C22×C22⋊C4C22×C4711yescharacteristic
495C22×C22⋊C4C22×C4711yescharacteristic
496C22×C22⋊C4C22×C4711yescharacteristic
497C22×C22⋊C4C22×C4711yescharacteristic
498C22×C42C22×C4712yescomplemented
499#388—28no—
500#380—24no—
501#379—24no—
502#379—24no—
503C4×C22⋊C4—24no—
504C2×#95C22×C4712yescomplemented
505C2×#95C22×C4712yescomplemented
506C2×#95C22×C4712yescomplemented
507C2×#95C22×C4712yescomplemented
508C2×#95C22×C4712yescomplemented
509C2×#95C22×C4712yescomplemented
510C47#1387311yescharacteristic, direct product factor, Sylow
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C4714yes—
522C25C23×C4711yescharacteristic
523C25C23×C4711yescharacteristic
524C25C23×C4711yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C4714yes—
534C23×C4C2×C4×C4714yes—
535C23×C4C23×C4712yes—
536C23×C4C23×C4712yes—
537C23×C4C23×C4711yescharacteristic
538C23×C4C23×C4711yescharacteristic
539C23×C4C23×C4712yes—
540C23×C4C23×C4712yes—
541C23×C4C23×C4711yescharacteristic
542C23×C4C23×C4711yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C4714yes—
573C2×C22⋊C4C2×C4×C4714yes—
574C2×C22⋊C4C2×C4×C4714yes—
575C2×C22⋊C4C2×C4×C4714yes—
576C2×C22⋊C4D4×C4714yes—
577C2×C22⋊C4D4×C4714yes—
578C2×C22⋊C4D4×C4718yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C4712yes—
634C24C22×C4×C4712yes—
635C24C22×C4×C4712yes—
636C24C2×D4×C4714yes—
637C24C2×D4×C4712yes—
638C24C2×D4×C4712yes—
639C24#41×C4714yes—
640C24#41×C4712yes—
641C24#41×C4712yes—
642C24#41×C4712yes—
643C24#41×C4712yes—
644C24C24×C4711yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C4712yes—
696C22×C4C22×C4×C4712yes—
697C22×C4C22×C4×C4712yes—
698C22×C4C22×C4×C4712yes—
699C22×C4C2×D4×C4714yes—
700C22×C4C2×D4×C4714yes—
701C22×C4C2×D4×C4714yes—
702C22×C4C2×D4×C4714yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C47116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—416no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—432no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23C2×C22⋊C4×C4714yes—
789C23#117×C4714yes—
790C23#117×C4714yes—
791C23C4×D4×C4714yes—
792C23C4×D4×C4714yes—
793C23#121×C4714yes—
794C23#123×C4714yes—
795C23#124×C4714yes—
796C23#126×C4714yes—
797C23C23×C4×C4711yescharacteristic
798C23C22×D4×C4712yes—
799C23C22×D4×C4711yescharacteristic
800C23C22×D4×C4711yescharacteristic
801C23C2×#41×C4711yescharacteristic
802C23C2×#41×C4711yescharacteristic
803C23C2×#41×C4712yes—
804C23C2×#41×C4711yescharacteristic
805C23C2×#41×C4711yescharacteristic
806C23H(5,𝔽2)×C4712yes—
807C23H(5,𝔽2)×C4712yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C4714yes—
857C2×C4C2×C22⋊C4×C4714yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—28no—
865C22—28no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22C47×#38818yescomplemented
892C22C22×C22⋊C4×C4711yescharacteristic
893C22C2×#117×C4711yescharacteristic
894C22C2×#117×C4711yescharacteristic
895C22C2×C4×D4×C4711yescharacteristic
896C22C2×C4×D4×C4711yescharacteristic
897C22C47×#51811yescharacteristic
898C22C47×#51811yescharacteristic
899C22C2×#121×C4711yescharacteristic
900C22C2×#123×C4711yescharacteristic
901C22C47×#52512yes—
902C22C47×#52512yes—
903C22C2×#124×C4711yescharacteristic
904C22C2×#126×C4711yescharacteristic
905C22C47×#53812yes—
906C22C47×#53812yes—
907C22D42×C4712yes—
908C22D42×C4712yes—
909C22C47×#54612yes—
910C22C47×#54612yes—
911C22C47×#54612yes—
912C22C47×#54612yes—
913C22C47×#55112yes—
914C22C47×#55112yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C47×#228011yescharacteristic
927C2C2×C47×#38811yescharacteristic
928C2C47×#231211yescharacteristic
929C2D4×C22⋊C4×C4711yescharacteristic
930C2D4×C22⋊C4×C4711yescharacteristic
931C2C47×#234211yescharacteristic
932C2C47×#234211yescharacteristic
933C2C47×#241812yes—
934C2C47×#242412yes—
935C2C47×#247212yes—
936C2C47×#248012yes—
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC26×C47C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#388C2semidirect
3. C2×C47×#380C2semidirect
6. C2×C4×C22⋊C4×C47C2semidirect
7. C47×#1440C2semidirect
8. C47×#1439C2semidirect
9. C47×#1437C2semidirect
10. C47×C22⋊#95C2semidirect
11. C47×C22⋊#95C2semidirect
15. C22×C4⋊C4×C47C22semidirect
17. C22×C22⋊C4×C47C4semidirect
30. C22×C42×C47C22semidirect
36. C2×#95×C47C22semidirect
37. C2×#95×C47C22semidirect
38. C2×#95×C47C22semidirect
39. C2×#95×C47C22semidirect
40. C2×#95×C47C22semidirect
41. C2×#95×C47C22semidirect
246. C22⋊C4×C47C22⋊C4semidirect
389. #13873C47direct (N × H)
423. C22×C47#388semidirect
456. C2×#388C2×C47semidirect
457. C2×#380C2×C47semidirect
460. C2×C4×C22⋊C4C2×C47semidirect
461. #1440C2×C47semidirect
462. #1439C2×C47semidirect
463. #1437C2×C47semidirect
464. C22⋊#95C2×C47semidirect
465. C22⋊#95C2×C47semidirect
483. C22×C4⋊C4C22×C47semidirect
485. C22×C22⋊C4C4×C47semidirect
498. C22×C42C22×C47semidirect
504. C2×#95C22×C47semidirect
505. C2×#95C22×C47semidirect
506. C2×#95C22×C47semidirect
507. C2×#95C22×C47semidirect
508. C2×#95C22×C47semidirect
509. C2×#95C22×C47semidirect
510. C47#13873direct (N × H)
715. C22⋊C4C22⋊C4×C47semidirect
891. C22C47×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C472
C2×C47×#3882
C2×C47×#3802
C2×C47×#3792
C2×C4×C22⋊C4×C472
C47×#14402
C47×#14392
C47×#14372
C47×C22⋊#952
#1387347