Finite Group Databasebeta

← #26139062

Subgroups — #26139062

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×D4×Dic47C211yesmaximal, characteristic
2C2×#15689003C211yesmaximal, characteristic
3C2×#15688986C211yesmaximal, characteristic, complemented
4C22×C47⋊#95C211yesmaximal, characteristic, complemented
5#20241641C212yesmaximal, complemented
6#20241637C212yesmaximal, complemented
7#20241620C212yesmaximal, complemented
8#20241610C212yesmaximal, complemented
9#20241610C211yesmaximal, characteristic, complemented
10#20241610C211yesmaximal, characteristic, complemented
11C22×#123×C47C211yesmaximal, characteristic
12C24×Dic47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C24×Dic47C2211yescharacteristic
15C2×D4×Dic47—24no—
16C2×D4×Dic47—24no—
17C2×D4×Dic47—24no—
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C22⋊Dic47C2211yescharacteristic
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2212yes—
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24#15689003—24no—
25#15688986—24no—
26C2×C47⋊#95—24no—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C23×D4×C47C2211yescharacteristic
37C24×C4×C47C2211yescharacteristic
38C2×#123×C47—24no—
39C2×#123×C47—24no—
40C2×#123×C47C418yescomplemented
41C22×C4⋊C4×C47C2212yes—
42C22×C22⋊C4×C47C2211yescharacteristic
43C22×C22⋊C4×C47C2212yes—
44C23×Dic47—22no—
45C23×Dic47—22no—
46C23×Dic47—22no—
47C23×Dic47—22no—
48C23×Dic47—22no—
49C23×Dic47—22no—
50C23×Dic47—24no—
51C23×Dic47—24no—
52C23×Dic47—22no—
53C23×Dic47—22no—
54C23×Dic47—24no—
55C23×Dic47—42no—
56C23×Dic47—42no—
57C23×Dic47—42no—
58C23×Dic47D414yes—
59C23×Dic47C2312yes—
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2312yes—
64C23×Dic47C2311yescharacteristic
65D4×Dic47—232no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—22no—
69C2×C22⋊Dic47—22no—
70C2×C22⋊Dic47—22no—
71C2×C22⋊Dic47—22no—
72C2×C22⋊Dic47—22no—
73C2×C22⋊Dic47—22no—
74C2×C22⋊Dic47—22no—
75C2×C22⋊Dic47—24no—
76C2×C22⋊Dic47—22no—
77C2×C22⋊Dic47—22no—
78C2×C22⋊Dic47—24no—
79C2×C22⋊Dic47—42no—
80C2×C22⋊Dic47D414yes—
81C2×C4×Dic47—22no—
82C2×C4×Dic47—22no—
83C2×C4×Dic47—22no—
84C47⋊#95—24no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C47⋊#95—24no—
88C47⋊#95—24no—
89C47⋊#95—24no—
90C47⋊#95—24no—
91C47⋊#95—42no—
92C47⋊#95—42no—
93C25×C47C2311yescharacteristic
94C25×C47C2311yescharacteristic
95C22×D4×C47—22no—
96C22×D4×C47—22no—
97C22×D4×C47—22no—
98C22×D4×C47—22no—
99C22×D4×C47C2×C414yes—
100C22×D4×C47D414yes—
101C22×D4×C47D414yes—
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×C47C2×C414yescomplemented
109C23×C4×C47C2312yes—
110C23×C4×C47C2312yes—
111C23×C4×C47C2311yescharacteristic
112#123×C47—232no—
113C2×C4⋊C4×C47—24no—
114C2×C4⋊C4×C47—24no—
115C2×C4⋊C4×C47C2×C418yescomplemented
116C2×C22⋊C4×C47—22no—
117C2×C22⋊C4×C47—22no—
118C2×C22⋊C4×C47—24no—
119C2×C22⋊C4×C47—24no—
120C2×C22⋊C4×C47C2×C414yescomplemented
121C2×C22⋊C4×C47C2×C418yescomplemented
122C24×C47—22no—
123C24×C47—22no—
124C24×C47—22no—
125C24×C47—22no—
126C24×C47—21no—
127C24×C47—21no—
128C24×C47—21no—
129C24×C47—21no—
130C24×C47—22no—
131C24×C47—22no—
132C24×C47—22no—
133C24×C47—22no—
134C24×C47C22×C412yes—
135C24×C47C22×C412yes—
136C24×C47C2×D412yes—
137C24×C47C2×D412yes—
138C24×C47C2×D412yes—
139C24×C47C2×D412yes—
140C24×C47C2×D412yes—
141C24×C47C2×D412yes—
142C24×C47#4112yes—
143C24×C47#4112yes—
144C24×C47C2411yescharacteristic
145C2×D4×C47—28no—
146C2×D4×C47—28no—
147C2×D4×C47—28no—
148C2×D4×C47—28no—
149C2×D4×C47—28no—
150C2×D4×C47—28no—
151C2×D4×C47C22⋊C4116yes—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—28no—
157C22×C4×C47—28no—
158C22×C4×C47—28no—
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—22no—
170C22×C4×C47—22no—
171C22×C4×C47—44no—
172C22×C4×C47—44no—
173C22×C4×C47—44no—
174C22×C4×C47—44no—
175C22×C4×C47C22×C414yes—
176C22×C4×C47C22×C414yes—
177C22×C4×C47C22×C412yes—
178C22×C4×C47C2×D412yes—
179C22×C4×C47C2×D412yes—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—22no—
183C22×Dic47—28no—
184C22×Dic47—28no—
185C22×Dic47—28no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—28no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—44no—
213C22×Dic47—48no—
214C22×Dic47—48no—
215C22×Dic47—48no—
216C22×Dic47—48no—
217C22×Dic47—48no—
218C22×Dic47—48no—
219C22×Dic47—44no—
220C22×Dic47—44no—
221C22×Dic47—44no—
222C22×Dic47—44no—
223C22×Dic47C2×D412yes—
224C22×Dic47C2×D412yes—
225C22×Dic47C2×D412yes—
226C22×Dic47C2×D412yes—
227C22×Dic47#4114yes—
228C22×Dic47#4114yes—
229C4⋊C4×C47—216no—
230C22⋊C4×C47—28no—
231C22⋊C4×C47—216no—
232C22⋊Dic47—28no—
233C22⋊Dic47—28no—
234C22⋊Dic47—48no—
235C22⋊Dic47—44no—
236C4⋊Dic47—28no—
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×C47—22no—
255C23×C47—22no—
256C23×C47—24no—
257C23×C47—24no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—24no—
263C23×C47—24no—
264C23×C47—24no—
265C23×C47—24no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—42no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—42no—
272C23×C47—42no—
273C23×C47—42no—
274C23×C47—42no—
275C23×C47—42no—
276C23×C47C2×C22⋊C414yes—
277C23×C47C2×C22⋊C414yes—
278C23×C47C4×D414yes—
279C23×C47C4×D414yes—
280C23×C47#12014yes—
281C23×C47#12114yes—
282C23×C47#12114yes—
283C23×C47#12314yes—
284C23×C47C23×C411yescharacteristic
285C23×C47C22×D411yescharacteristic
286C23×C47C22×D411yescharacteristic
287C23×C47C22×D411yescharacteristic
288C23×C47C22×D411yescharacteristic
289C23×C47C2×#4112yes—
290C23×C47C2×#4112yes—
291C23×C47C2×#4111yescharacteristic
292C23×C47C2×#4111yescharacteristic
293C23×C47H(5,𝔽2)12yes—
294C23×C472−1+412yes—
295D4×C47—232no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—24no—
303C2×C4×C47—24no—
304C2×C4×C47—24no—
305C2×C4×C47—24no—
306C2×C4×C47—24no—
307C2×C4×C47—24no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
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—416no—
317C2×C4×C47C2×C22⋊C414yes—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—24no—
321C2×Dic47—24no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—24no—
327C2×Dic47—22no—
328C2×Dic47—24no—
329C2×Dic47—24no—
330C2×Dic47—24no—
331C2×Dic47—24no—
332C2×Dic47—416no—
333C2×Dic47—416no—
334C2×Dic47—416no—
335C2×Dic47—42no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—42no—
340C2×Dic47—41no—
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×Dic47—42no—
354C2×Dic47#12314yescomplemented
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—28no—
367C22×C47—24no—
368C22×C47—42no—
369C22×C47—44no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—44no—
373C22×C47—44no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47#38618yes—
378C22×C47C22×C22⋊C411yescharacteristic
379C22×C47C2×C4×D411yescharacteristic
380C22×C47C2×C4×D411yescharacteristic
381C22×C47C4×#4112yes—
382C22×C47#52012yes—
383C22×C47C2×#12011yescharacteristic
384C22×C47C2×#12111yescharacteristic
385C22×C47C2×#12111yescharacteristic
386C22×C47C2×#12311yescharacteristic
387C22×C47C2×#12311yescharacteristic
388C22×C47#52511yescharacteristic
389C22×C47#52912yes—
390C22×C47#53411yescharacteristic
391C22×C47#53611yescharacteristic
392C22×C47#53912yes—
393C22×C47#54612yes—
394C22×C47#54612yes—
395C22×C47#54612yes—
396C22×C47#54712yes—
397C22×C47#54712yes—
398C22×C47#54712yes—
399C22×C47#55112yes—
400C22×C47#55212yes—
401C4×C47—24no—
402C4×C47—44no—
403C4×C47—44no—
404Dic47—24no—
405Dic47—42no—
406Dic47—42no—
407Dic47—42no—
408Dic47—44no—
409Dic47—82no—
410C22×#123D4711yescharacteristic
411C22×C4×D4—471no—
412C2×#386—471no—
413C2×#381—471no—
414C22×#95—471no—
415#1441—472no—
416#1440—472no—
417#1436—472no—
418C22⋊#95—471no—
419C22⋊#95—471no—
420C22⋊#95—472no—
421C2×C47—28no—
422C2×C47—44no—
423C2×C47C2×#38611yescharacteristic
424C2×C47C4×#12311yescharacteristic
425C2×C47#232211yescharacteristic
426C2×C47#233912yes—
427C2×C47#235912yes—
428C2×C47#240511yescharacteristic
429C2×C47#240611yescharacteristic
430C2×C47#241912yes—
431C2×C47#242512yes—
432C2×C47#248611yescharacteristic
433C2×C47#253411yescharacteristic
434C23×D4C2×D4711yescharacteristic
435C24×C4—471no—
436C24×C4—471no—
437C24×C4—471no—
438C24×C4C2×D4711yescharacteristic
439C2×#123—24no—
440C2×#123—24no—
441C2×#123Dic4718yescomplemented
442C2×C4×D4—944no—
443C2×C4×D4—944no—
444C2×C4×D4—944no—
445C22×C4⋊C4—471no—
446C22×C4⋊C4C2×D4712yes—
447C22×C22⋊C4—471no—
448C22×C22⋊C4—471no—
449C22×C22⋊C4—471no—
450C22×C22⋊C4—472no—
451C22×C22⋊C4C2×D4711yescharacteristic
452C22×C22⋊C4C2×D4712yes—
453C22×C42—471no—
454#386—944no—
455#381—944no—
456C2×#95—472no—
457C2×#95—472no—
458C2×#95—472no—
459C2×#95—472no—
460C2×#95—472no—
461C2×#95—472no—
462C2×#95—472no—
463C2×#95—472no—
464C2×#95—472no—
465C2×#95—944no—
466C47#1396811yescharacteristic, complemented, Sylow
467C25C22×D4711yescharacteristic
468C25C22×D4711yescharacteristic
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4C2×Dic4714yes—
474C22×D4C22⋊D4714yes—
475C22×D4C22⋊D4714yes—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—472no—
487C23×C4—474no—
488C23×C4—472no—
489C23×C4—942no—
490C23×C4—942no—
491C23×C4—944no—
492C23×C4—944no—
493C23×C4—944no—
494C23×C4—942no—
495C23×C4—942no—
496C23×C4—942no—
497C23×C4—942no—
498C23×C4—942no—
499C23×C4—942no—
500C23×C4—1882no—
501C23×C4—1882no—
502C23×C4—1882no—
503C23×C4C2×Dic4714yescomplemented
504C23×C4C22×D4712yes—
505C23×C4C22×D4712yes—
506C23×C4C22×D4711yescharacteristic
507#123—232no—
508C4×D4—9432no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—942no—
512C2×C4⋊C4—942no—
513C2×C4⋊C4—942no—
514C2×C4⋊C4C2×Dic4718yescomplemented
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—474no—
520C2×C22⋊C4—942no—
521C2×C22⋊C4—942no—
522C2×C22⋊C4—942no—
523C2×C22⋊C4—942no—
524C2×C22⋊C4—942no—
525C2×C22⋊C4—944no—
526C2×C22⋊C4—942no—
527C2×C22⋊C4—942no—
528C2×C22⋊C4—944no—
529C2×C22⋊C4—942no—
530C2×C22⋊C4—1882no—
531C2×C22⋊C4C2×Dic4714yescomplemented
532C2×C22⋊C4C2×Dic4718yescomplemented
533C2×C42—942no—
534C2×C42—942no—
535C2×C42—942no—
536#95—944no—
537#95—944no—
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—21no—
550C24—21no—
551C24—22no—
552C24—22no—
553C24—21no—
554C24—21no—
555C24—22no—
556C24—22no—
557C24D4×D4712yes—
558C24D4×D4712yes—
559C24#1062535212yes—
560C24#1062535212yes—
561C24C22×Dic4712yes—
562C24C22×Dic4712yes—
563C24C2×C22⋊D4712yes—
564C24C2×C22⋊D4712yes—
565C24C2×C22⋊D4712yes—
566C24C2×C22⋊D4712yes—
567C24C23×D4711yescharacteristic
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4C22⋊Dic47116yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—472no—
599C22×C4—474no—
600C22×C4—472no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—474no—
604C22×C4—948no—
605C22×C4—941no—
606C22×C4—941no—
607C22×C4—942no—
608C22×C4—948no—
609C22×C4—948no—
610C22×C4—948no—
611C22×C4—942no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—941no—
615C22×C4—942no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—942no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
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—1884no—
637C22×C4—1884no—
638C22×C4—1888no—
639C22×C4—1888no—
640C22×C4—1888no—
641C22×C4—1888no—
642C22×C4—1888no—
643C22×C4—1888no—
644C22×C4—1884no—
645C22×C4—1884no—
646C22×C4—1884no—
647C22×C4C22×Dic4714yes—
648C22×C4C22×Dic4714yes—
649C22×C4C22×Dic4712yes—
650C22×C4C2×C22⋊D4712yes—
651C22×C4C2×C22⋊D4712yes—
652C4⋊C4—216no—
653C4⋊C4—948no—
654C22⋊C4—28no—
655C22⋊C4—216no—
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—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—41no—
695C23—42no—
696C23—41no—
697C23—41no—
698C23—42no—
699C23C2×C22⋊Dic4714yes—
700C23C2×C22⋊Dic4714yes—
701C23D4×Dic4714yes—
702C23D4×Dic4714yes—
703C23#1309399214yes—
704C23#1309399614yes—
705C23#1309399614yes—
706C23#1309400514yes—
707C23C23×Dic4711yescharacteristic
708C23C2×D4×D4711yescharacteristic
709C23C2×D4×D4711yescharacteristic
710C23C22×C22⋊D4711yescharacteristic
711C23C22×C22⋊D4711yescharacteristic
712C23#41×D4712yes—
713C23#41×D4712yes—
714C23C2×#1062535211yescharacteristic
715C23C2×#1062535211yescharacteristic
716C23#1309407012yes—
717C23#1309407112yes—
718D4—232no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—416no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—474no—
741C2×C4—944no—
742C2×C4—944no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—944no—
746C2×C4—944no—
747C2×C4—944no—
748C2×C4—944no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—944no—
754C2×C4—942no—
755C2×C4—18816no—
756C2×C4—18816no—
757C2×C4—1882no—
758C2×C4—1882no—
759C2×C4—1882no—
760C2×C4—1882no—
761C2×C4—1882no—
762C2×C4—1882no—
763C2×C4—1882no—
764C2×C4—18816no—
765C2×C4—1882no—
766C2×C4—1882no—
767C2×C4—1882no—
768C2×C4—1882no—
769C2×C4—1882no—
770C2×C4—1882no—
771C2×C4—1882no—
772C2×C4—1881no—
773C2×C4—1881no—
774C2×C4—1881no—
775C2×C4—1882no—
776C2×C4—1881no—
777C2×C4C2×C22⋊Dic4714yes—
778C22—24no—
779C22—28no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—42no—
791C22—44no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22#1568900318yes—
800C22C22×C22⋊Dic4711yescharacteristic
801C22C2×D4×Dic4711yescharacteristic
802C22C2×D4×Dic4711yescharacteristic
803C22#41×Dic4712yes—
804C22#1568960612yes—
805C22C2×#1309399211yescharacteristic
806C22C2×#1309399611yescharacteristic
807C22C2×#1309399611yescharacteristic
808C22#123×D4711yescharacteristic
809C22C2×#1309400511yescharacteristic
810C22#1568963111yescharacteristic
811C22#1568965012yes—
812C22#1568968411yescharacteristic
813C22#1568969511yescharacteristic
814C22#1568971712yes—
815C22#1568976112yes—
816C22#1568976112yes—
817C22#1568976512yes—
818C22#1568977112yes—
819C22#1568977212yes—
820C22#1568977212yes—
821C22#1568979612yes—
822C22#1568981012yes—
823C4—24no—
824C4—44no—
825C4—44no—
826C4—944no—
827C4—3762no—
828C4—1882no—
829C4—1882no—
830C4—1882no—
831C4—1884no—
832C2—28no—
833C2—44no—
834C2C2×#1568900311yescharacteristic
835C2#123×Dic4711yescharacteristic
836C2#2024606011yescharacteristic
837C2#2024621812yes—
838C2#2024638412yes—
839C2#2024671211yescharacteristic
840C2#2024672011yescharacteristic
841C2#2024686112yes—
842C2#2024694312yes—
843C2#2024769311yescharacteristic
844C2#2024827711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×#123×C47C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC22×#123D47
hypocenterC47#13968
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
3. C2×#15688986C2semidirect
4. C22×C47⋊#95C2semidirect
5. #20241641C2semidirect
6. #20241637C2semidirect
7. #20241620C2semidirect
8. #20241610C2semidirect
9. #20241610C2semidirect
10. #20241610C2semidirect
40. C2×#123×C47C4semidirect
108. C23×C4×C47C2×C4semidirect
115. C2×C4⋊C4×C47C2×C4semidirect
120. C2×C22⋊C4×C47C2×C4semidirect
121. C2×C22⋊C4×C47C2×C4semidirect
354. C2×Dic47#123semidirect
441. C2×#123Dic47semidirect
466. C47#13968semidirect
503. C23×C4C2×Dic47semidirect
514. C2×C4⋊C4C2×Dic47semidirect
531. C2×C22⋊C4C2×Dic47semidirect
532. C2×C22⋊C4C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic472
C2×#156890032
C2×#156889862
C22×C47⋊#952
#202416412
#202416372
#202416202
#202416102
C22×#123×C472
#1396847