Finite Group Databasebeta

← #26139368

Subgroups — #26139368

Order 12032.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689021C211yesmaximal, characteristic, complemented
2C2×#15688983C211yesmaximal, characteristic
3C2×#15688983C211yesmaximal, characteristic
4C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
5#20241649C212yesmaximal, complemented
6#20241631C212yesmaximal
7#20241625C212yesmaximal
8#20241619C212yesmaximal, complemented
9#20241618C211yesmaximal, characteristic, complemented
10#20241618C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4⋊Dic47C2211yescharacteristic
16C22×Dic47⋊C4C2212yes—
17C22×C22⋊Dic47C2212yes—
18C22×C22⋊Dic47C2212yes—
19C22×C4×Dic47C2212yes—
20#15689021—24no—
21#15688983—24no—
22#15688983C418yescomplemented
23C4×C4⋊Dic47—24no—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C24×C4×C47C2211yescharacteristic
33C22×C22⋊C4×C47C2211yescharacteristic
34C22×C22⋊C4×C47C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C4×C22⋊C4×C47—24no—
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C23×Dic47C2312yes—
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2312yes—
44C2×C4⋊Dic47—22no—
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—22no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—22no—
53C2×C4⋊Dic47C2×C414yes—
54C2×C4⋊Dic47C2×C414yes—
55C2×C4⋊Dic47D414yes—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4—24no—
58C2×Dic47⋊C4—42no—
59C2×C22⋊Dic47—24no—
60C2×C22⋊Dic47—24no—
61C2×C22⋊Dic47—42no—
62C2×C22⋊Dic47—42no—
63C2×C22⋊Dic47—42no—
64C2×C22⋊Dic47C2×C418yes—
65C2×C4×Dic47—24no—
66C2×C4×Dic47—42no—
67C2×C4×Dic47—42no—
68C47⋊#95—24no—
69C47⋊#95—24no—
70C47⋊#95—24no—
71C47⋊#95—24no—
72C47⋊#95—42no—
73C47⋊#95—42no—
74C47⋊#95—42no—
75C47⋊#95C2×C418yes—
76C25×C47C2311yescharacteristic
77C23×C4×C47—22no—
78C23×C4×C47—22no—
79C23×C4×C47—22no—
80C23×C4×C47—22no—
81C23×C4×C47—22no—
82C23×C4×C47—22no—
83C23×C4×C47C2×C414yes—
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C2×C22⋊C4×C47—22no—
91C2×C22⋊C4×C47—22no—
92C2×C22⋊C4×C47—22no—
93C2×C22⋊C4×C47—22no—
94C2×C22⋊C4×C47—22no—
95C2×C22⋊C4×C47Q814yes—
96C2×C42×C47—22no—
97C2×C42×C47—22no—
98C2×C42×C47—22no—
99C2×C42×C47—22no—
100C2×C42×C47—22no—
101C2×C42×C47D414yes—
102#95×C47—22no—
103#95×C47—22no—
104C24×C47—21no—
105C24×C47—21no—
106C24×C47—21no—
107C24×C47—21no—
108C24×C47—21no—
109C24×C47—21no—
110C24×C47—21no—
111C24×C47—21no—
112C24×C47—21no—
113C24×C47—21no—
114C24×C47—21no—
115C24×C47—21no—
116C24×C47C22×C412yes—
117C24×C47C2×Q812yes—
118C24×C47#4112yes—
119C24×C47C2411yescharacteristic
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—28no—
149C22×C4×C47—28no—
150C22×C4×C47—28no—
151C22×C4×C47—44no—
152C22×C4×C47—44no—
153C22×C4×C47—44no—
154C22×C4×C47—44no—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C22×C412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×D412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×Q812yes—
162C22×C4×C47C2×Q812yes—
163C22×C4×C47#4112yes—
164C22×C4×C47#4112yes—
165C22×C4×C47#4112yes—
166C22×C4×C47#4112yes—
167C22×C4×C47#4112yes—
168C22×C4×C47#4112yes—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47C22×C414yes—
195C22×Dic47C22×C414yes—
196C22×Dic47C2×D414yes—
197C22⋊C4×C47—28no—
198C22⋊C4×C47—28no—
199C42×C47—28no—
200C42×C47—44no—
201C22⋊Dic47—48no—
202C22⋊Dic47—48no—
203C4⋊Dic47—28no—
204C4⋊Dic47—28no—
205C4⋊Dic47—28no—
206C4⋊Dic47—44no—
207Dic47⋊C4—48no—
208C4×Dic47—48no—
209C23×C47—22no—
210C23×C47—22no—
211C23×C47—22no—
212C23×C47—22no—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—22no—
221C23×C47—22no—
222C23×C47—22no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—22no—
227C23×C47—41no—
228C23×C47—41no—
229C23×C47—41no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47C4×Q814yes—
244C23×C47C23×C411yescharacteristic
245C23×C47C22×D411yescharacteristic
246C23×C47C22×D411yescharacteristic
247C23×C47C22×Q811yescharacteristic
248C23×C47C2×#4111yescharacteristic
249C23×C47C2×#4111yescharacteristic
250C23×C47C2×#4111yescharacteristic
251C23×C47C2×#4111yescharacteristic
252C23×C47C2×#4111yescharacteristic
253C23×C47C2×#4111yescharacteristic
254C23×C47C2×#4111yescharacteristic
255C23×C47H(5,𝔽2)11yescharacteristic
256C23×C47H(5,𝔽2)11yescharacteristic
257C23×C47H(5,𝔽2)11yescharacteristic
258C23×C472−1+411yescharacteristic
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—416no—
294C2×C4×C47#11714yes—
295C2×C4×C47C4×D414yes—
296C2×C4×C47C4×D414yes—
297C2×C4×C47#12114yes—
298C2×C4×C47C22⋊Q814yes—
299C2×C4×C47#12314yes—
300C2×C4×C47#12414yes—
301C2×C4×C47#12614yes—
302C2×Dic47—24no—
303C2×Dic47—24no—
304C2×Dic47—24no—
305C2×Dic47—24no—
306C2×Dic47—24no—
307C2×Dic47—24no—
308C2×Dic47—24no—
309C2×Dic47—24no—
310C2×Dic47—24no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330#13993—471nomaximal, Sylow
331C22×C47—24no—
332C22×C47—24no—
333C22×C47—24no—
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—42no—
337C22×C47—42no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47C2×#11711yescharacteristic
347C22×C47C2×C4×D411yescharacteristic
348C22×C47C2×C4×D411yescharacteristic
349C22×C47C2×C4×Q811yescharacteristic
350C22×C47C4×#4111yescharacteristic
351C22×C47#51811yescharacteristic
352C22×C47#52011yescharacteristic
353C22×C47C2×#12111yescharacteristic
354C22×C47C2×C22⋊Q811yescharacteristic
355C22×C47C2×#12311yescharacteristic
356C22×C47#52511yescharacteristic
357C22×C47C2×#12411yescharacteristic
358C22×C47C2×#12611yescharacteristic
359C22×C47#52911yescharacteristic
360C22×C47#53311yescharacteristic
361C22×C47#53511yescharacteristic
362C22×C47#53711yescharacteristic
363C22×C47#54011yescharacteristic
364C22×C47#54211yescharacteristic
365C22×C47#54611yescharacteristic
366C22×C47#54611yescharacteristic
367C22×C47D4×Q811yescharacteristic
368C22×C47#55011yescharacteristic
369C22×C47#55211yescharacteristic
370C22×C47#55311yescharacteristic
371C22×C47#55311yescharacteristic
372C22×C47#55311yescharacteristic
373C22×C47#55311yescharacteristic
374C22×C47#55311yescharacteristic
375C22×C47#55411yescharacteristic
376C22×C47#55411yescharacteristic
377C22×C47#55411yescharacteristic
378C22×C47#55511yescharacteristic
379C22×C47#55611yescharacteristic
380C22×C47#55611yescharacteristic
381C4×C47—24no—
382C4×C47—42no—
383C4×C47—42no—
384C4×C47—42no—
385C4×C47—42no—
386C4×C47#38818yes—
387Dic47—44no—
388Dic47—44no—
389Dic47—44no—
390Dic47—82no—
391C2×#389—471no—
392C2×#380—471no—
393C2×#380—471no—
394C2×C4×C4⋊C4—471no—
395C2×C4×C22⋊C4D4711yescharacteristic
396#1443—472no—
397#1439—472no—
398#1437—472no—
399#1436—472no—
400C4⋊#95—471no—
401C4⋊#95—471no—
402C2×C47—44no—
403C2×C47C2×#38811yescharacteristic
404C2×C47C4×C22⋊Q811yescharacteristic
405C2×C47#232411yescharacteristic
406C2×C47#234511yescharacteristic
407C2×C47#234711yescharacteristic
408C2×C47#236011yescharacteristic
409C2×C47#236311yescharacteristic
410C2×C47#248511yescharacteristic
411C2×C47#248711yescharacteristic
412C2×C47#249011yescharacteristic
413C2×C47#249211yescharacteristic
414C2×C47#249411yescharacteristic
415C2×C47#249711yescharacteristic
416C2×C47#253511yescharacteristic
417C2×C47#253811yescharacteristic
418C24×C4C2×D4711yescharacteristic
419C22×C4⋊C4—471no—
420C22×C4⋊C4—471no—
421C22×C4⋊C4—471no—
422C22×C4⋊C4—471no—
423C22×C4⋊C4—472no—
424C22×C22⋊C4—472no—
425C22×C22⋊C4—472no—
426C22×C22⋊C4C2×D4711yescharacteristic
427C22×C22⋊C4C2×D4711yescharacteristic
428C22×C42—472no—
429C22×C42C2×D4711yescharacteristic
430C22×C42C2×D4711yescharacteristic
431#389—944no—
432#380—478no—
433#380—944no—
434C4×C4⋊C4—944no—
435C4×C22⋊C4—24no—
436C2×#95—472no—
437C2×#95—472no—
438C2×#95—472no—
439C2×#95—472no—
440C2×#95—472no—
441C2×#95—472no—
442C2×#95—472no—
443C2×#95—472no—
444C2×#95C2×D4711yescharacteristic
445C2×#95C2×D4711yescharacteristic
446C47#1399311yescharacteristic, complemented, Sylow
447C25C22×D4711yescharacteristic
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—472no—
455C23×C4—472no—
456C23×C4—472no—
457C23×C4—472no—
458C23×C4C4×D4714yes—
459C23×C4C22×D4711yescharacteristic
460C23×C4C22×D4711yescharacteristic
461C23×C4C22×D4711yescharacteristic
462C23×C4C22×D4711yescharacteristic
463C23×C4C22×D4711yescharacteristic
464C23×C4C22×D4711yescharacteristic
465C2×C4⋊C4—474no—
466C2×C4⋊C4—474no—
467C2×C4⋊C4—474no—
468C2×C4⋊C4—942no—
469C2×C4⋊C4—942no—
470C2×C4⋊C4—942no—
471C2×C4⋊C4—942no—
472C2×C4⋊C4—942no—
473C2×C4⋊C4—942no—
474C2×C4⋊C4—944no—
475C2×C4⋊C4—944no—
476C2×C4⋊C4—942no—
477C2×C4⋊C4—942no—
478C2×C4⋊C4—942no—
479C2×C4⋊C4—1882no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—478no—
486C2×C22⋊C4—944no—
487C2×C22⋊C4—944no—
488C2×C22⋊C4—1882no—
489C2×C22⋊C4—1882no—
490C2×C22⋊C4—1882no—
491C2×C22⋊C4Dic9414yes—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—944no—
498C2×C42—1882no—
499C2×C42—1882no—
500C2×C42C22⋊D4714yes—
501#95—22no—
502#95—22no—
503#95—478no—
504#95—944no—
505#95—944no—
506#95—944no—
507#95—944no—
508#95—1882no—
509#95—1882no—
510#95—1882no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24C2×Dic9412yes—
524C24C2×C4×D4712yes—
525C24#1062535012yes—
526C24C23×D4711yescharacteristic
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—474no—
563C22×C4—474no—
564C22×C4—474no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4C2×Dic9412yes—
591C22×C4C2×Dic9412yes—
592C22×C4C2×C4×D4712yes—
593C22×C4C2×C4×D4712yes—
594C22×C4#1062535012yes—
595C22×C4#1062535012yes—
596C22×C4#1062535012yes—
597C22×C4D4×D4712yes—
598C22×C4#1062535212yes—
599C22×C4#1062535212yes—
600C22×C4#1062535212yes—
601C22×C4C2×C22⋊D4712yes—
602C22×C4C2×C22⋊D4712yes—
603C22×C4C2×C22⋊D4712yes—
604C4⋊C4—948no—
605C4⋊C4—948no—
606C4⋊C4—948no—
607C4⋊C4—1888no—
608C4⋊C4—1884no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—1888no—
612C22⋊C4—1888no—
613C42—28no—
614C42—44no—
615C42—1888no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C4×Dic9414yes—
651C23C22×C4×D4711yescharacteristic
652C23C2×D4×D4711yescharacteristic
653C23C22×C22⋊D4711yescharacteristic
654C23C22×Dic9411yescharacteristic
655C23C2×#1062535211yescharacteristic
656C23C2×#1062535211yescharacteristic
657C23C2×#1062535211yescharacteristic
658C23C2×#1062535011yescharacteristic
659C23C2×#1062535011yescharacteristic
660C23C2×#1062535011yescharacteristic
661C23C2×#1062535011yescharacteristic
662C23#1309407011yescharacteristic
663C23#1309407011yescharacteristic
664C23#1309407011yescharacteristic
665C23#1309407111yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—416no—
701C2×C4—944no—
702C2×C4—944no—
703C2×C4—944no—
704C2×C4—944no—
705C2×C4—944no—
706C2×C4—944no—
707C2×C4—944no—
708C2×C4—944no—
709C2×C4—944no—
710C2×C4—1882no—
711C2×C4—1882no—
712C2×C4—1882no—
713C2×C4—1882no—
714C2×C4—1882no—
715C2×C4—1882no—
716C2×C4—1882no—
717C2×C4—1882no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4—1882no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4—1882no—
728C2×C4—1882no—
729C2×C4#1309398014yes—
730C2×C4(C22⋊D47)⋊C414yes—
731C2×C4C4×C22⋊D4714yes—
732C2×C4#1309399514yes—
733C2×C4#1309400314yes—
734C2×C4#1309400514yes—
735C2×C4#1309401014yes—
736C2×C4#1309401714yes—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×#1309398011yescharacteristic
753C22C2×(C22⋊D47)⋊C411yescharacteristic
754C22C2×C4×C22⋊D4711yescharacteristic
755C22C2×C4×Dic9411yescharacteristic
756C22C4×#1062535011yescharacteristic
757C22#1568959711yescharacteristic
758C22#1568960311yescharacteristic
759C22C2×#1309399511yescharacteristic
760C22C2×#1309400311yescharacteristic
761C22C2×#1309400511yescharacteristic
762C22#1568963411yescharacteristic
763C22C2×#1309401011yescharacteristic
764C22C2×#1309401711yescharacteristic
765C22#1568965711yescharacteristic
766C22#1568968011yescharacteristic
767C22#1568968711yescharacteristic
768C22#1568970111yescharacteristic
769C22#1568972811yescharacteristic
770C22#1568974411yescharacteristic
771C22#1568976911yescharacteristic
772C22#1568976911yescharacteristic
773C22D4×Dic9411yescharacteristic
774C22#1568979411yescharacteristic
775C22#1568981311yescharacteristic
776C22#1568981911yescharacteristic
777C22#1568981911yescharacteristic
778C22#1568981911yescharacteristic
779C22#1568981911yescharacteristic
780C22#1568981911yescharacteristic
781C22#1568983011yescharacteristic
782C22#1568983011yescharacteristic
783C22#1568983011yescharacteristic
784C22#1568983811yescharacteristic
785C22#1568984311yescharacteristic
786C22#1568984311yescharacteristic
787C4—24no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—3762no—
793C4—1884no—
794C4—1884no—
795C4—1884no—
796C4#1568901118yes—
797C2—44no—
798C2C2×#1568901111yescharacteristic
799C2C4×#1309400311yescharacteristic
800C2#2024608111yescharacteristic
801C2#2024626311yescharacteristic
802C2#2024627911yescharacteristic
803C2#2024639111yescharacteristic
804C2#2024642411yescharacteristic
805C2#2024768511yescharacteristic
806C2#2024770511yescharacteristic
807C2#2024774011yescharacteristic
808C2#2024776211yescharacteristic
809C2#2024778811yescharacteristic
810C2#2024782111yescharacteristic
811C2#2024828911yescharacteristic
812C2#2024831011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×C4×C22⋊C4D47
hypocenterC47#13993
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#15689021C2semidirect
4. C2×C4×C4⋊Dic47C2semidirect
5. #20241649C2semidirect
8. #20241619C2semidirect
9. #20241618C2semidirect
10. #20241618C2semidirect
22. #15688983C4semidirect
446. C47#13993semidirect

Maximal subgroups

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

subgroupindex
C2×#156890212
C2×#156889832
C2×C4×C4⋊Dic472
#202416492
#202416312
#202416252
#202416192
#202416182
C2×C4×C22⋊C4×C472
#1399347