Finite Group Databasebeta

← #26139077

Subgroups — #26139077

Order 12032.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093995C211yesmaximal, characteristic
2C2×#15689026C211yesmaximal, characteristic, complemented
3C2×#15689002C212yesmaximal, complemented
4C2×#15688980C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
6#20241635C212yesmaximal, complemented
7#20241627C212yesmaximal, complemented
8#20241618C211yesmaximal, characteristic, complemented
9#20241617C211yesmaximal, characteristic, complemented
10#20241611C212yesmaximal, complemented
11C22×C4×D4×C47C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2212yes—
13C23×C4×D47C2211yescharacteristic
14C2×#13093995—24no—
15C2×#13093995—24no—
16C2×#13093995C418yescomplemented
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C22⋊Dic47C2212yes—
20C22×C22⋊Dic47C2212yes—
21C22×C22⋊Dic47C2212yes—
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2212yes—
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26#15689026—24no—
27#15689002—28no—
28#15688980—24no—
29C4×(C2×D47)⋊C4—24no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C23×D4×C47C2211yescharacteristic
38C24×C4×C47C2212yes—
39C2×C4×D4×C47—24no—
40C2×C4×D4×C47—24no—
41C2×C4×D4×C47—24no—
42C22×C4⋊C4×C47C2211yescharacteristic
43C22×C22⋊C4×C47C2212yes—
44C22×C42×C47C2211yescharacteristic
45C24×D47C2311yescharacteristic
46C22×C22⋊D47—24no—
47C22×C22⋊D47—24no—
48C22×C22⋊D47—24no—
49C22×C22⋊D47—24no—
50C22×C22⋊D47—42no—
51C22×C22⋊D47—42no—
52C22×C22⋊D47C2×C418yescomplemented
53C23×Dic47C2312yes—
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2312yes—
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C22×C4×D47—22no—
59C22×C4×D47—22no—
60C22×C4×D47—22no—
61C22×C4×D47—22no—
62C22×C4×D47—22no—
63C22×C4×D47—22no—
64C22×C4×D47C2×C414yescomplemented
65#13093995—232no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—22no—
69C2×C4⋊Dic47—22no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47C2×C414yescomplemented
72C2×C22⋊Dic47—24no—
73C2×C22⋊Dic47—24no—
74C2×C22⋊Dic47—24no—
75C2×C22⋊Dic47—24no—
76C2×C22⋊Dic47—24no—
77C2×C22⋊Dic47—24no—
78C2×C22⋊Dic47—42no—
79C2×C22⋊Dic47—42no—
80C2×C22⋊Dic47C2×C418yescomplemented
81C2×(C2×D47)⋊C4—22no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—22no—
85C2×(C2×D47)⋊C4—22no—
86C2×(C2×D47)⋊C4—24no—
87C2×(C2×D47)⋊C4—24no—
88C2×(C2×D47)⋊C4—42no—
89C2×(C2×D47)⋊C4D414yescomplemented
90C2×C4×Dic47—22no—
91C2×C4×Dic47—22no—
92C2×C4×Dic47—22no—
93C47⋊#95—22no—
94C47⋊#95—22no—
95C47⋊#95—24no—
96C47⋊#95—24no—
97C47⋊#95—24no—
98C47⋊#95—42no—
99C47⋊#95—42no—
100C25×C47C2312yes—
101C22×D4×C47—22no—
102C22×D4×C47—22no—
103C22×D4×C47—22no—
104C22×D4×C47—22no—
105C22×D4×C47C2×C414yes—
106C22×D4×C47D414yes—
107C22×D4×C47D414yes—
108C23×C4×C47—24no—
109C23×C4×C47—24no—
110C23×C4×C47—24no—
111C23×C4×C47—24no—
112C23×C4×C47—24no—
113C23×C4×C47—42no—
114C23×C4×C47—42no—
115C23×C4×C47C2311yescharacteristic
116C23×C4×C47C2312yes—
117C23×C4×C47C2311yescharacteristic
118C23×C4×C47C2311yescharacteristic
119C4×D4×C47—232no—
120C2×C4⋊C4×C47—22no—
121C2×C4⋊C4×C47—22no—
122C2×C4⋊C4×C47D414yescomplemented
123C2×C22⋊C4×C47—24no—
124C2×C22⋊C4×C47—24no—
125C2×C22⋊C4×C47—24no—
126C2×C42×C47—22no—
127C2×C42×C47—22no—
128C2×C42×C47D414yescomplemented
129C24×C47—22no—
130C24×C47—22no—
131C24×C47—22no—
132C24×C47—22no—
133C24×C47—22no—
134C24×C47—22no—
135C24×C47—22no—
136C24×C47—22no—
137C24×C47—22no—
138C24×C47—22no—
139C24×C47—22no—
140C24×C47—22no—
141C24×C47C22×C414yes—
142C24×C47C2×D414yes—
143C24×C47C2×D414yes—
144C24×C47C2411yescharacteristic
145C23×D47—21no—
146C23×D47—21no—
147C23×D47—21no—
148C23×D47—21no—
149C23×D47—21no—
150C23×D47—21no—
151C23×D47—21no—
152C23×D47—21no—
153C23×D47—21no—
154C23×D47—21no—
155C23×D47—21no—
156C23×D47—21no—
157C23×D47C22×C412yes—
158C23×D47C2×D412yes—
159C23×D47#4112yes—
160C2×D4×C47—28no—
161C2×D4×C47—28no—
162C2×D4×C47—28no—
163C2×D4×C47—28no—
164C2×D4×C47—28no—
165C2×D4×C47—28no—
166C2×D4×C47C22⋊C4116yescomplemented
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—216no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—48no—
185C22×C4×C47—48no—
186C22×C4×C47—48no—
187C22×C4×C47—48no—
188C22×C4×C47—48no—
189C22×C4×C47—48no—
190C22×C4×C47C22×C412yes—
191C22×C4×C47C2×D412yes—
192C22×C4×C47C2×D414yes—
193C22×C4×C47C2×D412yes—
194C22×C4×C47C2×D412yes—
195C22×C4×C47C2×D412yes—
196C22×C4×C47C2×D412yes—
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2×D412yes—
199C22×C4×C47#4112yes—
200C22×C4×C47#4112yes—
201C22×C4×C47#4112yes—
202C2×C22⋊D47—216no—
203C2×C22⋊D47—216no—
204C2×C22⋊D47—48no—
205C2×C22⋊D47—48no—
206C2×C22⋊D47—48no—
207C2×C22⋊D47—48no—
208C2×C22⋊D47—48no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—22no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—22no—
227C22×Dic47—21no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47C22×C412yes—
241C22×Dic47C22×C414yes—
242C22×Dic47C2×D412yes—
243C22×Dic47#4112yes—
244C2×C4×D47—28no—
245C2×C4×D47—28no—
246C2×C4×D47—28no—
247C2×C4×D47—44no—
248C2×C4×D47—44no—
249C2×C4×D47—44no—
250C2×C4×D47—44no—
251C4⋊C4×C47—28no—
252C22⋊C4×C47—216no—
253C42×C47—28no—
254C22⋊Dic47—216no—
255C22⋊Dic47—48no—
256C22⋊Dic47—48no—
257(C2×D47)⋊C4—28no—
258(C2×D47)⋊C4—28no—
259(C2×D47)⋊C4—48no—
260C4⋊Dic47—28no—
261C4⋊Dic47—44no—
262C4×Dic47—44no—
263C23×C47—24no—
264C23×C47—24no—
265C23×C47—24no—
266C23×C47—24no—
267C23×C47—24no—
268C23×C47—24no—
269C23×C47—24no—
270C23×C47—24no—
271C23×C47—24no—
272C23×C47—24no—
273C23×C47—24no—
274C23×C47—24no—
275C23×C47—24no—
276C23×C47—24no—
277C23×C47—24no—
278C23×C47—24no—
279C23×C47—24no—
280C23×C47—24no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47—42no—
285C23×C47—42no—
286C23×C47—42no—
287C23×C47—42no—
288C23×C47—42no—
289C23×C47—42no—
290C23×C47—42no—
291C23×C47—42no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47—42no—
295C23×C47—42no—
296C23×C47—42no—
297C23×C47C2×C22⋊C418yes—
298C23×C47C23×C411yescharacteristic
299C23×C47C22×D411yescharacteristic
300C23×C47C22×D411yescharacteristic
301C23×C47C22×D411yescharacteristic
302C23×C47C22×D411yescharacteristic
303C23×C47C22×D411yescharacteristic
304C23×C47C2×#4111yescharacteristic
305C23×C47C2×#4111yescharacteristic
306C23×C47C2×#4111yescharacteristic
307C23×C47C2×#4111yescharacteristic
308C23×C47C2×#4111yescharacteristic
309C23×C47H(5,𝔽2)11yescharacteristic
310C23×C47H(5,𝔽2)11yescharacteristic
311C23×C47H(5,𝔽2)11yescharacteristic
312C23×C472−1+411yescharacteristic
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—41no—
332C22×D47—41no—
333C22×D47—41no—
334C22×D47—41no—
335C22×D47—41no—
336C22×D47—41no—
337C22×D47—41no—
338C22×D47—41no—
339C22×D47—41no—
340C22×D47—41no—
341C22×D47—41no—
342C22×D47—41no—
343C22×D47—41no—
344C22×D47—41no—
345C22×D47—41no—
346C22×D47—41no—
347C22×D47C4×D414yescomplemented
348D4×C47—232no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—24no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—24no—
360C2×C4×C47—24no—
361C2×C4×C47—432no—
362C2×C4×C47—42no—
363C2×C4×C47—42no—
364C2×C4×C47—42no—
365C2×C4×C47—41no—
366C2×C4×C47—42no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47C2×C22⋊C414yes—
371C2×C4×C47C4×D414yes—
372C2×C4×C47C4×D414yes—
373C2×C4×C47#12014yes—
374C2×C4×C47#12114yes—
375C2×C4×C47#12114yes—
376C2×C4×C47#12114yescomplemented
377C2×C4×C47#12314yes—
378C22⋊D47—432no—
379C2×Dic47—24no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—24no—
384C2×Dic47—24no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—41no—
392C2×Dic47—41no—
393C2×Dic47—41no—
394C2×Dic47—41no—
395C2×Dic47—41no—
396C2×Dic47—41no—
397C2×Dic47—41no—
398C2×Dic47—41no—
399C2×Dic47—42no—
400C2×Dic47—42no—
401C2×Dic47—41no—
402C2×Dic47—42no—
403C2×Dic47—42no—
404C2×Dic47—41no—
405C2×Dic47—41no—
406C2×Dic47—41no—
407C2×Dic47—42no—
408C2×Dic47—42no—
409C2×Dic47—42no—
410C2×Dic47—42no—
411C2×Dic47—42no—
412C2×Dic47—42no—
413C2×Dic47—42no—
414C4×D47—416no—
415#13970—471nomaximal, Sylow
416C22×C47—28no—
417C22×C47—28no—
418C22×C47—28no—
419C22×C47—44no—
420C22×C47—44no—
421C22×C47—44no—
422C22×C47—44no—
423C22×C47—44no—
424C22×C47—44no—
425C22×C47—44no—
426C22×C47—44no—
427C22×C47—44no—
428C22×C47—44no—
429C22×C47—44no—
430C22×C47—44no—
431C22×C47C22×C22⋊C411yescharacteristic
432C22×C47C2×C4×D411yescharacteristic
433C22×C47C2×C4×D411yescharacteristic
434C22×C47C2×C4×D411yescharacteristic
435C22×C47C4×#4111yescharacteristic
436C22×C47#51811yescharacteristic
437C22×C47#52011yescharacteristic
438C22×C47C2×#12011yescharacteristic
439C22×C47C2×#12111yescharacteristic
440C22×C47C2×#12111yescharacteristic
441C22×C47C2×#12111yescharacteristic
442C22×C47C2×#12311yescharacteristic
443C22×C47#52511yescharacteristic
444C22×C47#52911yescharacteristic
445C22×C47#53211yescharacteristic
446C22×C47#53511yescharacteristic
447C22×C47#53711yescharacteristic
448C22×C47#54011yescharacteristic
449C22×C47#54211yescharacteristic
450C22×C47D4211yescharacteristic
451C22×C47D4211yescharacteristic
452C22×C47D4211yescharacteristic
453C22×C47#54611yescharacteristic
454C22×C47#54611yescharacteristic
455C22×C47#54611yescharacteristic
456C22×C47#54611yescharacteristic
457C22×C47#54611yescharacteristic
458C22×C47#54711yescharacteristic
459C22×C47#54711yescharacteristic
460C22×C47#54711yescharacteristic
461C22×C47#54811yescharacteristic
462C22×C47#55011yescharacteristic
463C22×C47#55311yescharacteristic
464C22×C47#55311yescharacteristic
465C22×C47#55511yescharacteristic
466C2×D47—24no—
467C2×D47—24no—
468C2×D47—24no—
469C2×D47—42no—
470C2×D47—42no—
471C2×D47—42no—
472C2×D47—42no—
473C2×D47—42no—
474C2×D47—42no—
475C2×D47—42no—
476C2×D47—42no—
477C2×D47—42no—
478C2×D47—42no—
479C2×D47—42no—
480C2×D47—42no—
481C4×C47—24no—
482C4×C47—42no—
483C4×C47—44no—
484C4×C47#38618yescomplemented
485Dic47—44no—
486Dic47—42no—
487Dic47—42no—
488Dic47—42no—
489Dic47—82no—
490C22×#121—471no—
491C22×C4×D4D4711yescharacteristic, complemented
492C2×#390—471no—
493C2×#386—472no—
494C2×#380—471no—
495C2×C4×C22⋊C4—471no—
496#1440—472no—
497#1438—472no—
498C4⋊#95—471no—
499C4⋊#95—471no—
500C22⋊#95—472no—
501C2×C47—48no—
502C2×C47C2×#38611yescharacteristic
503C2×C47C4×#12111yescharacteristic
504C2×C47#232411yescharacteristic
505C2×C47D4×C22⋊C411yescharacteristic
506C2×C47#233911yescharacteristic
507C2×C47#236111yescharacteristic
508C2×C47#236311yescharacteristic
509C2×C47#240711yescharacteristic
510C2×C47#240811yescharacteristic
511C2×C47#242011yescharacteristic
512C2×C47#242211yescharacteristic
513C2×C47#242711yescharacteristic
514C2×C47#242811yescharacteristic
515C2×C47#253511yescharacteristic
516C2×C47#253711yescharacteristic
517D47—44no—
518C23×D4—472no—
519C23×D4C2×D4711yescharacteristic
520C24×C4—471no—
521C24×C4C2×D4712yes—
522C2×#121—478no—
523C2×#121—944no—
524C2×#121—944no—
525C2×C4×D4—24no—
526C2×C4×D4—24no—
527C2×C4×D4—24no—
528C22×C4⋊C4—471no—
529C22×C4⋊C4—471no—
530C22×C4⋊C4C2×D4711yescharacteristic
531C22×C22⋊C4—472no—
532C22×C22⋊C4—471no—
533C22×C22⋊C4—471no—
534C22×C22⋊C4—472no—
535C22×C22⋊C4—472no—
536C22×C22⋊C4—472no—
537C22×C22⋊C4C2×D4712yes—
538C22×C42—471no—
539C22×C42C2×D4711yescharacteristic
540#390—944no—
541#386—948no—
542#380—944no—
543C4×C22⋊C4—944no—
544C2×#95—471no—
545C2×#95—472no—
546C2×#95—472no—
547C2×#95—472no—
548C2×#95—471no—
549C2×#95—472no—
550C2×#95—472no—
551C47#1397011yescharacteristic, complemented, Sylow
552C25—471no—
553C25C22×D4712yes—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—478no—
559C22×D4—944no—
560C22×D4—944no—
561C22×D4—944no—
562C22×D4—944no—
563C22×D4—1882no—
564C22×D4—1882no—
565C22×D4C4×D4714yes—
566C22×D4D18814yes—
567C22×D4C22⋊D4714yes—
568C23×C4—24no—
569C23×C4—24no—
570C23×C4—24no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4—471no—
576C23×C4—471no—
577C23×C4—471no—
578C23×C4—472no—
579C23×C4—474no—
580C23×C4—472no—
581C23×C4—942no—
582C23×C4—942no—
583C23×C4—942no—
584C23×C4—942no—
585C23×C4—942no—
586C23×C4—942no—
587C23×C4C22×D4711yescharacteristic
588C23×C4C22×D4712yes—
589C23×C4C22×D4711yescharacteristic
590C23×C4C22×D4711yescharacteristic
591#121—9432no—
592C4×D4—232no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—474no—
596C2×C4⋊C4—942no—
597C2×C4⋊C4—942no—
598C2×C4⋊C4—942no—
599C2×C4⋊C4—942no—
600C2×C4⋊C4—942no—
601C2×C4⋊C4C22⋊D4714yescomplemented
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—478no—
606C2×C22⋊C4—474no—
607C2×C22⋊C4—942no—
608C2×C22⋊C4—942no—
609C2×C22⋊C4—944no—
610C2×C22⋊C4—944no—
611C2×C22⋊C4—942no—
612C2×C22⋊C4—942no—
613C2×C22⋊C4—942no—
614C2×C22⋊C4—944no—
615C2×C22⋊C4—944no—
616C2×C22⋊C4—944no—
617C2×C22⋊C4—944no—
618C2×C22⋊C4—944no—
619C2×C22⋊C4—944no—
620C2×C22⋊C4—1882no—
621C2×C22⋊C4—1882no—
622C2×C22⋊C4—1882no—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—942no—
626C2×C42—942no—
627C2×C42—942no—
628C2×C42C22⋊D4714yescomplemented
629#95—944no—
630#95—944no—
631#95—942no—
632#95—942no—
633#95—944no—
634#95—1882no—
635#95—1882no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—472no—
649C24—472no—
650C24—472no—
651C24—941no—
652C24—941no—
653C24—941no—
654C24—941no—
655C24—941no—
656C24—941no—
657C24—941no—
658C24—941no—
659C24—941no—
660C24—941no—
661C24—941no—
662C24—941no—
663C24C2×C4×D4714yes—
664C24C2×D18814yes—
665C24C2×C22⋊D4714yes—
666C24C23×D4711yescharacteristic
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—9416no—
674C2×D4—9416no—
675C2×D4—1888no—
676C2×D4—1888no—
677C2×D4—1888no—
678C2×D4—1888no—
679C2×D4—1888no—
680C2×D4(C2×D47)⋊C4116yescomplemented
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—216no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—48no—
699C22×C4—48no—
700C22×C4—48no—
701C22×C4—48no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—472no—
705C22×C4—474no—
706C22×C4—472no—
707C22×C4—472no—
708C22×C4—942no—
709C22×C4—941no—
710C22×C4—941no—
711C22×C4—941no—
712C22×C4—941no—
713C22×C4—941no—
714C22×C4—942no—
715C22×C4—941no—
716C22×C4—941no—
717C22×C4—941no—
718C22×C4—942no—
719C22×C4—941no—
720C22×C4—942no—
721C22×C4—941no—
722C22×C4—941no—
723C22×C4—941no—
724C22×C4—941no—
725C22×C4—941no—
726C22×C4—941no—
727C22×C4—942no—
728C22×C4—941no—
729C22×C4—942no—
730C22×C4—941no—
731C22×C4—941no—
732C22×C4—948no—
733C22×C4—948no—
734C22×C4—948no—
735C22×C4—942no—
736C22×C4—942no—
737C22×C4—942no—
738C22×C4—942no—
739C22×C4—942no—
740C22×C4—942no—
741C22×C4—942no—
742C22×C4—1884no—
743C22×C4—1884no—
744C22×C4—1884no—
745C22×C4—1884no—
746C22×C4C2×C4×D4712yes—
747C22×C4C2×D18812yes—
748C22×C4#1062535012yes—
749C22×C4#1062535012yes—
750C22×C4D4×D4712yes—
751C22×C4#1062535212yes—
752C22×C4C2×C22⋊D4712yes—
753C22×C4C2×C22⋊D4714yes—
754C22×C4C2×C22⋊D4712yes—
755C22×C4C2×C22⋊D4712yes—
756C22×C4C2×C22⋊D4712yes—
757C22×C4C2×C22⋊D4712yes—
758C4⋊C4—28no—
759C4⋊C4—948no—
760C4⋊C4—1884no—
761C22⋊C4—216no—
762C22⋊C4—948no—
763C22⋊C4—9416no—
764C22⋊C4—948no—
765C22⋊C4—1888no—
766C22⋊C4—1888no—
767C22⋊C4—1888no—
768C42—28no—
769C42—1884no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—474no—
805C23—942no—
806C23—942no—
807C23—942no—
808C23—942no—
809C23—942no—
810C23—942no—
811C23—942no—
812C23—942no—
813C23—942no—
814C23—942no—
815C23—942no—
816C23—942no—
817C23—942no—
818C23—942no—
819C23—942no—
820C23—942no—
821C23—942no—
822C23—942no—
823C23—1881no—
824C23—1881no—
825C23—1881no—
826C23—1881no—
827C23—1881no—
828C23—1881no—
829C23—1881no—
830C23—1881no—
831C23—1881no—
832C23—1881no—
833C23—1881no—
834C23—1881no—
835C23—1881no—
836C23—1881no—
837C23—1881no—
838C23—1881no—
839C23C2×(C2×D47)⋊C418yes—
840C23C22×C4×D4711yescharacteristic
841C23C2×D4×D4711yescharacteristic
842C23C22×C22⋊D4711yescharacteristic
843C23C22×C22⋊D4711yescharacteristic
844C23C22×C22⋊D4711yescharacteristic
845C23C22×D18811yescharacteristic
846C23#41×D4711yescharacteristic
847C23#41×D4711yescharacteristic
848C23C2×#1062535211yescharacteristic
849C23C2×#1062535011yescharacteristic
850C23C2×#1062535011yescharacteristic
851C23#1309406911yescharacteristic
852C23#1309406911yescharacteristic
853C23#1309407011yescharacteristic
854C23#1309407111yescharacteristic
855D4—232no—
856D4—18832no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—432no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—42no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—942no—
879C2×C4—942no—
880C2×C4—942no—
881C2×C4—942no—
882C2×C4—942no—
883C2×C4—944no—
884C2×C4—944no—
885C2×C4—942no—
886C2×C4—942no—
887C2×C4—944no—
888C2×C4—942no—
889C2×C4—942no—
890C2×C4—1882no—
891C2×C4—1882no—
892C2×C4—1882no—
893C2×C4—1882no—
894C2×C4—1882no—
895C2×C4—1882no—
896C2×C4—1882no—
897C2×C4—1882no—
898C2×C4—1882no—
899C2×C4—1882no—
900C2×C4—1881no—
901C2×C4—1882no—
902C2×C4—1881no—
903C2×C4—1881no—
904C2×C4—1881no—
905C2×C4—1881no—
906C2×C4—1881no—
907C2×C4—1881no—
908C2×C4—1881no—
909C2×C4—1881no—
910C2×C4—1881no—
911C2×C4—1881no—
912C2×C4—1881no—
913C2×C4—18816no—
914C2×C4C2×(C2×D47)⋊C414yes—
915C2×C4C4×C22⋊D4714yes—
916C2×C4C4×C22⋊D4714yes—
917C2×C4#1309399314yes—
918C2×C4#1309399514yescomplemented
919C2×C4#1309399814yes—
920C2×C4#1309399814yes—
921C2×C4#1309400714yes—
922C22—28no—
923C22—28no—
924C22—28no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—44no—
933C22—44no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—944no—
938C22—944no—
939C22—944no—
940C22—1882no—
941C22—1882no—
942C22—1882no—
943C22—1882no—
944C22—1882no—
945C22—1882no—
946C22—1882no—
947C22—1882no—
948C22—1882no—
949C22—1882no—
950C22—1882no—
951C22—1882no—
952C22C22×(C2×D47)⋊C411yescharacteristic
953C22C4×D4×D4711yescharacteristic
954C22C2×C4×C22⋊D4711yescharacteristic
955C22C2×C4×C22⋊D4711yescharacteristic
956C22C4×#1062535211yescharacteristic
957C22#1568959511yescharacteristic
958C22#1568960211yescharacteristic
959C22C2×#1309399311yescharacteristic
960C22C2×#1309399511yescharacteristic
961C22C2×#1309399811yescharacteristic
962C22C2×#1309399811yescharacteristic
963C22C2×#1309400711yescharacteristic
964C22#1568963011yescharacteristic
965C22#1568965511yescharacteristic
966C22#1568967011yescharacteristic
967C22#1568969011yescharacteristic
968C22#1568970111yescharacteristic
969C22#1568972411yescharacteristic
970C22#1568973811yescharacteristic
971C22D4×C22⋊D4711yescharacteristic
972C22D4×C22⋊D4711yescharacteristic
973C22D4×D18811yescharacteristic
974C22#1568976111yescharacteristic
975C22#1568976711yescharacteristic
976C22#1568976711yescharacteristic
977C22#1568976811yescharacteristic
978C22#1568976811yescharacteristic
979C22#1568977211yescharacteristic
980C22#1568977711yescharacteristic
981C22#1568977811yescharacteristic
982C22#1568978011yescharacteristic
983C22#1568979211yescharacteristic
984C22#1568982311yescharacteristic
985C22#1568982311yescharacteristic
986C22#1568983811yescharacteristic
987C4—24no—
988C4—42no—
989C4—44no—
990C4—3762no—
991C4—1882no—
992C4—1884no—
993C4—1882no—
994C4—1882no—
995C4#1568900218yescomplemented
996C2—48no—
997C2—1884no—
998C2C2×#1568900211yescharacteristic
999C2C4×#1309399511yescharacteristic
1000C2#2024607511yescharacteristic
1001C2D4×(C2×D47)⋊C411yescharacteristic
1002C2#2024621311yescharacteristic
1003C2#2024640011yescharacteristic
1004C2#2024642211yescharacteristic
1005C2#2024672711yescharacteristic
1006C2#2024673811yescharacteristic
1007C2#2024687411yescharacteristic
1008C2#2024689611yescharacteristic
1009C2#2024695911yescharacteristic
1010C2#2024697011yescharacteristic
1011C2#2024828511yescharacteristic
1012C2#2024830111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×C4×D4×C47C2
socle, cosocleC24×C47C24
prime radicalC22×#13093995C2
hypercenterC22×C4×D4D47
hypocenterC47#13970
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#15689026C2semidirect
3. C2×#15689002C2semidirect
4. C2×#15688980C2semidirect
5. C2×C4×(C2×D47)⋊C4C2semidirect
6. #20241635C2semidirect
7. #20241627C2semidirect
8. #20241618C2semidirect
9. #20241617C2semidirect
10. #20241611C2semidirect
11. C22×C4×D4×C47C2semidirect
16. C2×#13093995C4semidirect
52. C22×C22⋊D47C2×C4semidirect
64. C22×C4×D47C2×C4semidirect
71. C2×C4⋊Dic47C2×C4semidirect
80. C2×C22⋊Dic47C2×C4semidirect
89. C2×(C2×D47)⋊C4D4semidirect
122. C2×C4⋊C4×C47D4semidirect
128. C2×C42×C47D4semidirect
166. C2×D4×C47C22⋊C4semidirect
347. C22×D47C4×D4semidirect
376. C2×C4×C47#121semidirect
484. C4×C47#386semidirect
491. C22×C4×D4D47semidirect
551. C47#13970semidirect
601. C2×C4⋊C4C22⋊D47semidirect
628. C2×C42C22⋊D47semidirect
680. C2×D4(C2×D47)⋊C4semidirect
918. C2×C4#13093995semidirect
995. C4#15689002semidirect

Maximal subgroups

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

subgroupindex
C22×#130939952
C2×#156890262
C2×#156890022
C2×#156889802
C2×C4×(C2×D47)⋊C42
#202416352
#202416272
#202416182
#202416172
#202416112
C22×C4×D4×C472
#1397047