Finite Group Databasebeta

← #26139059

Subgroups — #26139059

Order 12032.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094007C211yesmaximal, characteristic
2C22×C4×C22⋊D47C211yesmaximal, characteristic
3C2×#15689002C211yesmaximal, characteristic
4C2×#15688986C211yesmaximal, characteristic, complemented
5#20241639C212yesmaximal, complemented
6#20241636C212yesmaximal, complemented
7#20241619C212yesmaximal, complemented
8#20241611C211yesmaximal, characteristic, complemented
9#20241611C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C22×#95×C47C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C2×#13094007—24no—
15C2×#13094007—24no—
16C2×#13094007C418yescomplemented
17C2×C4×C22⋊D47—24no—
18C2×C4×C22⋊D47—24no—
19C2×C4×C22⋊D47—24no—
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2212yes—
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2212yes—
27C22×(C2×D47)⋊C4C2212yes—
28C22×C4×Dic47C2211yescharacteristic
29#15689002—24no—
30#15688986—24no—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C2×C47⋊#95C2212yes—
38C24×C4×C47C2211yescharacteristic
39C24×C4×C47C2211yescharacteristic
40C24×C4×C47C2211yescharacteristic
41C2×#95×C47—24no—
42C2×#95×C47C2212yes—
43C2×#95×C47C2212yes—
44C24×D47C2311yescharacteristic
45C22×C22⋊D47—22no—
46C22×C22⋊D47—22no—
47C22×C22⋊D47—22no—
48C22×C22⋊D47—22no—
49C22×C22⋊D47C2×C414yes—
50C22×C22⋊D47D414yes—
51C22×C22⋊D47D414yes—
52C23×Dic47C2312yes—
53C23×Dic47C2312yes—
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C22×C4×D47—22no—
58C22×C4×D47—22no—
59C22×C4×D47—22no—
60C22×C4×D47—24no—
61C22×C4×D47—42no—
62#13094007—232no—
63C4×C22⋊D47—232no—
64C2×Dic47⋊C4—22no—
65C2×Dic47⋊C4—22no—
66C2×Dic47⋊C4—22no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4—24no—
69C2×Dic47⋊C4C2×C418yescomplemented
70C2×C22⋊Dic47—22no—
71C2×C22⋊Dic47—22no—
72C2×C22⋊Dic47—22no—
73C2×C22⋊Dic47—22no—
74C2×C22⋊Dic47—22no—
75C2×C22⋊Dic47—22no—
76C2×C22⋊Dic47—22no—
77C2×C22⋊Dic47C2×C414yescomplemented
78C2×C22⋊Dic47D414yes—
79C2×(C2×D47)⋊C4—22no—
80C2×(C2×D47)⋊C4—24no—
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—24no—
85C2×(C2×D47)⋊C4—24no—
86C2×(C2×D47)⋊C4—42no—
87C2×(C2×D47)⋊C4C2×C418yescomplemented
88C2×C4×Dic47—22no—
89C2×C4×Dic47—22no—
90C2×C4×Dic47—22no—
91C47⋊#95—24no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—24no—
95C47⋊#95—24no—
96C47⋊#95—42no—
97C47⋊#95—42no—
98C25×C47C2311yescharacteristic
99C23×C4×C47—22no—
100C23×C4×C47—22no—
101C23×C4×C47—22no—
102C23×C4×C47—22no—
103C23×C4×C47—22no—
104C23×C4×C47—22no—
105C23×C4×C47—22no—
106C23×C4×C47—22no—
107C23×C4×C47—22no—
108C23×C4×C47—24no—
109C23×C4×C47—24no—
110C23×C4×C47—22no—
111C23×C4×C47—22no—
112C23×C4×C47—42no—
113C23×C4×C47—42no—
114C23×C4×C47C2×C414yescomplemented
115C23×C4×C47D414yes—
116C23×C4×C47C2312yes—
117C23×C4×C47C2311yescharacteristic
118C23×C4×C47C2312yes—
119C23×C4×C47C2311yescharacteristic
120#95×C47—24no—
121#95×C47—24no—
122C24×C47—22no—
123C24×C47—22no—
124C24×C47—22no—
125C24×C47—22no—
126C24×C47C22×C412yes—
127C24×C47C2×D412yes—
128C24×C47C2×D412yes—
129C24×C47C2×D412yes—
130C24×C47C2×D412yes—
131C24×C47#4112yes—
132C24×C47#4112yes—
133C24×C47C2411yescharacteristic
134C23×D47—21no—
135C23×D47—21no—
136C23×D47—22no—
137C23×D47—22no—
138C23×D47—21no—
139C23×D47—21no—
140C23×D47—22no—
141C23×D47—22no—
142C23×D47C22×C412yes—
143C23×D47C2×D412yes—
144C23×D47C2×D412yes—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—22no—
148C22×C4×C47—28no—
149C22×C4×C47—28no—
150C22×C4×C47—28no—
151C22×C4×C47—28no—
152C22×C4×C47—28no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—28no—
170C22×C4×C47—44no—
171C22×C4×C47—48no—
172C22×C4×C47—48no—
173C22×C4×C47—48no—
174C22×C4×C47—48no—
175C22×C4×C47—44no—
176C22×C4×C47—44no—
177C22×C4×C47—44no—
178C22×C4×C47—44no—
179C22×C4×C47—44no—
180C22×C4×C47—44no—
181C22×C4×C47C22×C414yes—
182C22×C4×C47C2×D412yes—
183C22×C4×C47C2×D412yes—
184C22×C4×C47#4114yes—
185C22×C4×C47#4114yes—
186C2×C22⋊D47—28no—
187C2×C22⋊D47—28no—
188C2×C22⋊D47—28no—
189C2×C22⋊D47—28no—
190C2×C22⋊D47—28no—
191C2×C22⋊D47—28no—
192C2×C22⋊D47C22⋊C4116yes—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47C22×C414yes—
219C22×Dic47C22×C412yes—
220C22×Dic47C2×D412yes—
221C22×Dic47C2×D412yes—
222C22×Dic47C2×D412yes—
223C22×Dic47C2×D412yes—
224C2×C4×D47—28no—
225C2×C4×D47—48no—
226C2×C4×D47—48no—
227C2×C4×D47—44no—
228C2×C4×D47—44no—
229C22⋊Dic47—28no—
230C22⋊Dic47—28no—
231C22⋊Dic47—44no—
232(C2×D47)⋊C4—28no—
233(C2×D47)⋊C4—216no—
234(C2×D47)⋊C4—48no—
235Dic47⋊C4—28no—
236Dic47⋊C4—216no—
237C4×Dic47—28no—
238C23×C47—24no—
239C23×C47—24no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—24no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—24no—
246C23×C47—24no—
247C23×C47—24no—
248C23×C47—24no—
249C23×C47—24no—
250C23×C47—24no—
251C23×C47—24no—
252C23×C47—24no—
253C23×C47—24no—
254C23×C47C2×C22⋊C414yes—
255C23×C47C4×D414yes—
256C23×C47C4×D414yes—
257C23×C47#12014yes—
258C23×C47#12114yes—
259C23×C47#12114yes—
260C23×C47#12314yes—
261C23×C47C23×C411yescharacteristic
262C23×C47C22×D411yescharacteristic
263C23×C47C22×D411yescharacteristic
264C23×C47C22×D411yescharacteristic
265C23×C47C22×D411yescharacteristic
266C23×C47C2×#4111yescharacteristic
267C23×C47C2×#4111yescharacteristic
268C23×C47C2×#4112yes—
269C23×C47C2×#4112yes—
270C23×C47H(5,𝔽2)12yes—
271C23×C472−1+412yes—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—24no—
275C22×D47—24no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—24no—
281C22×D47—24no—
282C22×D47—24no—
283C22×D47—24no—
284C22×D47—41no—
285C22×D47—41no—
286C22×D47—42no—
287C22×D47—41no—
288C22×D47—41no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47C2×C22⋊C414yes—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—24no—
298C2×C4×C47—24no—
299C2×C4×C47—24no—
300C2×C4×C47—24no—
301C2×C4×C47—24no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—24no—
305C2×C4×C47—22no—
306C2×C4×C47—24no—
307C2×C4×C47—24no—
308C2×C4×C47—416no—
309C2×C4×C47—416no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—416no—
321C2×C4×C47#12314yescomplemented
322C22⋊D47—232no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—24no—
330C2×Dic47—24no—
331C2×Dic47—24no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—24no—
335C2×Dic47—24no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—42no—
351C2×Dic47—42no—
352C2×Dic47—42no—
353C2×Dic47C2×C22⋊C414yes—
354C4×D47—416no—
355#13968—471nomaximal, Sylow
356C22×C47—24no—
357C22×C47—28no—
358C22×C47—28no—
359C22×C47—24no—
360C22×C47—24no—
361C22×C47—28no—
362C22×C47—28no—
363C22×C47—24no—
364C22×C47—24no—
365C22×C47—24no—
366C22×C47#38618yes—
367C22×C47C22×C22⋊C411yescharacteristic
368C22×C47C2×C4×D411yescharacteristic
369C22×C47C2×C4×D411yescharacteristic
370C22×C47C4×#4112yes—
371C22×C47#52012yes—
372C22×C47C2×#12011yescharacteristic
373C22×C47C2×#12111yescharacteristic
374C22×C47C2×#12111yescharacteristic
375C22×C47C2×#12311yescharacteristic
376C22×C47C2×#12311yescharacteristic
377C22×C47#52511yescharacteristic
378C22×C47#52912yes—
379C22×C47#53411yescharacteristic
380C22×C47#53611yescharacteristic
381C22×C47#53912yes—
382C22×C47#54612yes—
383C22×C47#54612yes—
384C22×C47#54612yes—
385C22×C47#54712yes—
386C22×C47#54712yes—
387C22×C47#54712yes—
388C22×C47#55112yes—
389C22×C47#55212yes—
390C2×D47—28no—
391C2×D47—24no—
392C2×D47—42no—
393C2×D47—44no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—44no—
397C2×D47—44no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C4×C47—24no—
402C4×C47—42no—
403C4×C47—44no—
404C4×C47—44no—
405Dic47—24no—
406Dic47—44no—
407Dic47—42no—
408Dic47—42no—
409Dic47—82no—
410C22×#123—471no—
411C22×C4×D4—471no—
412C2×#386—471no—
413C2×#381—471no—
414C22×#95D4711yescharacteristic, complemented
415#1441—472no—
416#1440—472no—
417#1436—472no—
418C22⋊#95—472no—
419C22⋊#95—471no—
420C22⋊#95—471no—
421C2×C47—28no—
422C2×C47C2×#38611yescharacteristic
423C2×C47C4×#12311yescharacteristic
424C2×C47#232211yescharacteristic
425C2×C47#233912yes—
426C2×C47#235912yes—
427C2×C47#240511yescharacteristic
428C2×C47#240611yescharacteristic
429C2×C47#241912yes—
430C2×C47#242512yes—
431C2×C47#248611yescharacteristic
432C2×C47#253411yescharacteristic
433D47—44no—
434C23×D4—471no—
435C24×C4—471no—
436C24×C4C2×D4711yescharacteristic
437C24×C4C2×D4711yescharacteristic
438C24×C4C2×D4711yescharacteristic
439C2×#123—478no—
440C2×#123—944no—
441C2×#123—944no—
442C2×C4×D4—944no—
443C2×C4×D4—944no—
444C2×C4×D4—944no—
445C22×C4⋊C4—472no—
446C22×C4⋊C4—471no—
447C22×C22⋊C4—471no—
448C22×C22⋊C4—471no—
449C22×C22⋊C4—472no—
450C22×C22⋊C4—471no—
451C22×C22⋊C4—471no—
452C22×C22⋊C4—472no—
453C22×C42—471no—
454#386—944no—
455#381—944no—
456C2×#95—24no—
457C2×#95—472no—
458C2×#95—472no—
459C2×#95—472no—
460C2×#95—472no—
461C2×#95—472no—
462C2×#95—472no—
463C2×#95—472no—
464C2×#95C2×D4712yes—
465C2×#95C2×D4712yes—
466C47#1396811yescharacteristic, complemented, Sylow
467C25—471no—
468C25C22×D4711yescharacteristic
469C22×D4—474no—
470C22×D4—474no—
471C22×D4—474no—
472C22×D4—942no—
473C22×D4—942no—
474C22×D4—942no—
475C22×D4—942no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—24no—
486C23×C4—24no—
487C23×C4—22no—
488C23×C4—22no—
489C23×C4—42no—
490C23×C4—42no—
491C23×C4—471no—
492C23×C4—472no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—472no—
496C23×C4—942no—
497C23×C4—942no—
498C23×C4—942no—
499C23×C4—944no—
500C23×C4—1882no—
501C23×C4C4×D4714yescomplemented
502C23×C4C22⋊D4714yes—
503C23×C4C22×D4712yes—
504C23×C4C22×D4712yes—
505C23×C4C22×D4711yescharacteristic
506C23×C4C22×D4711yescharacteristic
507#123—9432no—
508C4×D4—9432no—
509C2×C4⋊C4—478no—
510C2×C4⋊C4—942no—
511C2×C4⋊C4—942no—
512C2×C4⋊C4—944no—
513C2×C4⋊C4—944no—
514C2×C4⋊C4—942no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—478no—
518C2×C22⋊C4—942no—
519C2×C22⋊C4—942no—
520C2×C22⋊C4—944no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—942no—
523C2×C22⋊C4—942no—
524C2×C22⋊C4—942no—
525C2×C22⋊C4—942no—
526C2×C22⋊C4—942no—
527C2×C22⋊C4—944no—
528C2×C22⋊C4—942no—
529C2×C22⋊C4—942no—
530C2×C22⋊C4—942no—
531C2×C22⋊C4—944no—
532C2×C22⋊C4—1882no—
533C2×C42—942no—
534C2×C42—942no—
535C2×C42—942no—
536#95—24no—
537#95—24no—
538#95—944no—
539#95—944no—
540#95—944no—
541#95—944no—
542#95—944no—
543#95—1882no—
544#95—1882no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—472no—
550C24—472no—
551C24—472no—
552C24—941no—
553C24—941no—
554C24—941no—
555C24—942no—
556C24—942no—
557C24—941no—
558C24—942no—
559C24—942no—
560C24C2×C4×D4712yes—
561C24#1062535012yes—
562C24D4×D4712yes—
563C24D4×D4712yes—
564C24D4×D4712yes—
565C24#1062535212yes—
566C24C2×C22⋊D4712yes—
567C24C23×D4711yescharacteristic
568C2×D4—4716no—
569C2×D4—948no—
570C2×D4—948no—
571C2×D4—948no—
572C2×D4—948no—
573C2×D4—948no—
574C2×D4—948no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—28no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—472no—
612C22×C4—472no—
613C22×C4—472no—
614C22×C4—474no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—948no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—941no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—942no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—1888no—
644C22×C4—1888no—
645C22×C4—1884no—
646C22×C4—1884no—
647C22×C4C2×C4×D4714yes—
648C22×C4#1062535014yes—
649C22×C4#1062535014yes—
650C22×C4C2×C22⋊D4712yes—
651C22×C4C2×C22⋊D4712yes—
652C4⋊C4—9416no—
653C4⋊C4—948no—
654C22⋊C4—9416no—
655C22⋊C4—948no—
656C22⋊C4—948no—
657C22⋊C4—948no—
658C22⋊C4—1888no—
659C22⋊C4—1884no—
660C42—948no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—474no—
678C23—944no—
679C23—944no—
680C23—944no—
681C23—944no—
682C23—942no—
683C23—942no—
684C23—944no—
685C23—944no—
686C23—942no—
687C23—942no—
688C23—942no—
689C23—942no—
690C23—1882no—
691C23—1882no—
692C23—1882no—
693C23—1882no—
694C23—1881no—
695C23—1881no—
696C23—1882no—
697C23—1881no—
698C23—1881no—
699C23—1882no—
700C23C22⋊C4×D4714yes—
701C23(C22⋊D47)⋊C414yes—
702C23C4×C22⋊D4714yes—
703C23#1309399214yes—
704C23#1309399514yes—
705C23#1309399714yes—
706C23#1309400614yes—
707C23C22×C4×D4711yescharacteristic
708C23C2×D4×D4711yescharacteristic
709C23C2×D4×D4711yescharacteristic
710C23C2×D4×D4711yescharacteristic
711C23C22×C22⋊D4711yescharacteristic
712C23C2×#1062535211yescharacteristic
713C23C2×#1062535012yes—
714C23C2×#1062535012yes—
715C23C2×#1062535011yescharacteristic
716C23#1309406912yes—
717C23#1309407212yes—
718D4—9432no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—416no—
733C2×C4—416no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—416no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—474no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—944no—
753C2×C4—944no—
754C2×C4—944no—
755C2×C4—944no—
756C2×C4—944no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—18816no—
760C2×C4—1882no—
761C2×C4—1882no—
762C2×C4—1882no—
763C2×C4—1882no—
764C2×C4—1882no—
765C2×C4—1882no—
766C2×C4—1882no—
767C2×C4—1882no—
768C2×C4—1882no—
769C2×C4—1882no—
770C2×C4—1882no—
771C2×C4—1882no—
772C2×C4—1882no—
773C2×C4—1881no—
774C2×C4—1881no—
775C2×C4—1881no—
776C2×C4—1881no—
777C2×C4#1309400714yescomplemented
778C22—24no—
779C22—28no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—24no—
788C22—944no—
789C22—948no—
790C22—1882no—
791C22—1884no—
792C22—1884no—
793C22—1882no—
794C22—1882no—
795C22—1884no—
796C22—1882no—
797C22—1882no—
798C22—1882no—
799C22#1568899918yes—
800C22C2×C22⋊C4×D4711yescharacteristic
801C22C2×(C22⋊D47)⋊C411yescharacteristic
802C22C2×C4×C22⋊D4711yescharacteristic
803C22C4×#1062535012yes—
804C22#1568960412yes—
805C22C2×#1309399211yescharacteristic
806C22C2×#1309399511yescharacteristic
807C22C2×#1309399711yescharacteristic
808C22C2×#1309400611yescharacteristic
809C22C2×#1309400711yescharacteristic
810C22#1568963411yescharacteristic
811C22#1568965712yes—
812C22#1568968211yescharacteristic
813C22#1568969711yescharacteristic
814C22#1568972012yes—
815C22#1568976312yes—
816C22#1568976312yes—
817C22#1568976312yes—
818C22#1568977412yes—
819C22#1568977412yes—
820C22#1568977412yes—
821C22#1568979912yes—
822C22#1568980812yes—
823C4—24no—
824C4—44no—
825C4—42no—
826C4—44no—
827C4—944no—
828C4—3762no—
829C4—1882no—
830C4—1882no—
831C4—1884no—
832C2—28no—
833C2—1884no—
834C2C2×#1568899911yescharacteristic
835C2C4×#1309400711yescharacteristic
836C2#2024605711yescharacteristic
837C2#2024621512yes—
838C2#2024637612yes—
839C2#2024671511yescharacteristic
840C2#2024672311yescharacteristic
841C2#2024686512yes—
842C2#2024693912yes—
843C2#2024769011yescharacteristic
844C2#2024827811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC22×#95D47
hypocenterC47#13968
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
4. C2×#15688986C2semidirect
5. #20241639C2semidirect
6. #20241636C2semidirect
7. #20241619C2semidirect
8. #20241611C2semidirect
9. #20241611C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C22×#95×C47C2semidirect
16. C2×#13094007C4semidirect
69. C2×Dic47⋊C4C2×C4semidirect
77. C2×C22⋊Dic47C2×C4semidirect
87. C2×(C2×D47)⋊C4C2×C4semidirect
114. C23×C4×C47C2×C4semidirect
321. C2×C4×C47#123semidirect
414. C22×#95D47semidirect
466. C47#13968semidirect
501. C23×C4C4×D47semidirect
777. C2×C4#13094007semidirect

Maximal subgroups

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

subgroupindex
C22×#130940072
C22×C4×C22⋊D472
C2×#156890022
C2×#156889862
#202416392
#202416362
#202416192
#202416112
(C2×D47)⋊#952
C22×#95×C472
#1396847