Finite Group Databasebeta

← #26153024

Subgroups — #26153024

Order 12032.

1778 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689052C212yesmaximal, complemented
2C2×#15689025C211yesmaximal, characteristic
3C2×#15689024C211yesmaximal, characteristic
4C2×#15689024C211yesmaximal, characteristic
5C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
6#20241636C212yesmaximal, complemented
7#20241636C212yesmaximal, complemented
8#20241632C212yesmaximal, complemented
9#20241617C211yesmaximal, characteristic, complemented
10#20241617C211yesmaximal, characteristic, complemented
11C47×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×Dic47⋊C4C2211yescharacteristic
15C22×Dic47⋊C4C2211yescharacteristic
16C22×(C2×D47)⋊C4C2212yes—
17C22×(C2×D47)⋊C4C2212yes—
18C22×(C2×D47)⋊C4C2212yes—
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21C22×(C2×D47)⋊C4C2212yes—
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24#15689052—28no—
25#15689025—24no—
26#15689024—24no—
27#15689024—24no—
28C4×Dic47⋊C4—24no—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C2×#95×C47C2212yes—
39C2×#95×C47C2212yes—
40C24×D47C2312yes—
41C22×D188—22no—
42C22×D188—22no—
43C22×D188—22no—
44C22×D188—22no—
45C22×D188—22no—
46C22×D188—22no—
47C22×D188D414yes—
48C23×Dic47C2312yes—
49C23×Dic47C2311yescharacteristic
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2311yescharacteristic
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47—22no—
56C2×Dic47⋊C4—22no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4D414yescomplemented
62C2×(C2×D47)⋊C4—24no—
63C2×(C2×D47)⋊C4—24no—
64C2×(C2×D47)⋊C4—24no—
65C2×(C2×D47)⋊C4—24no—
66C2×(C2×D47)⋊C4—24no—
67C2×(C2×D47)⋊C4—24no—
68C2×(C2×D47)⋊C4—24no—
69C2×(C2×D47)⋊C4—24no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—24no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—24no—
74C2×(C2×D47)⋊C4—42no—
75C2×(C2×D47)⋊C4—42no—
76C2×(C2×D47)⋊C4—42no—
77C2×(C2×D47)⋊C4—42no—
78C2×(C2×D47)⋊C4—42no—
79C2×(C2×D47)⋊C4—42no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47—22no—
82C2×C4×Dic47—22no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47D414yes—
86C47⋊#95—22no—
87C47⋊#95—22no—
88C47⋊#95—24no—
89C47⋊#95—24no—
90C47⋊#95—42no—
91C47⋊#95—42no—
92C23×C4×C47C2312yes—
93C23×C4×C47C2312yes—
94C23×C4×C47C2311yescharacteristic
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47—22no—
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47—22no—
103C2×C42×C47—22no—
104C2×C42×C47—22no—
105C2×C42×C47—22no—
106#95×C47—24no—
107#95×C47—42no—
108C24×C47C2411yescharacteristic
109C23×D47—22no—
110C23×D47—22no—
111C23×D47—22no—
112C23×D47—22no—
113C23×D47—22no—
114C23×D47—22no—
115C23×D47—22no—
116C23×D47—22no—
117C23×D47—22no—
118C23×D47—22no—
119C23×D47—22no—
120C23×D47—22no—
121C23×D47—22no—
122C23×D47—22no—
123C23×D47C2×D414yes—
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—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47C2×D412yes—
151C22×C4×C47C2×D412yes—
152C22×C4×C47C2×D412yes—
153C22×C4×C47#4112yes—
154C22×C4×C47#4112yes—
155C22×C4×C47#4112yes—
156C22×C4×C47#4112yes—
157C22×C4×C47#4112yes—
158C22×C4×C47#4112yes—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47C2×D412yes—
189C22×Dic47C2×D412yes—
190C22×Dic47C2×D412yes—
191C22×Dic47C2×D412yes—
192C22×Dic47#4112yes—
193C22×Dic47#4112yes—
194C2×D188—28no—
195C2×D188—28no—
196C2×D188—28no—
197C2×D188—44no—
198C2×D188—44no—
199C2×D188—44no—
200C2×D188—44no—
201C4⋊C4×C47—44no—
202C4⋊C4×C47—44no—
203C42×C47—44no—
204(C2×D47)⋊C4—48no—
205(C2×D47)⋊C4—48no—
206(C2×D47)⋊C4—48no—
207(C2×D47)⋊C4—48no—
208(C2×D47)⋊C4—48no—
209(C2×D47)⋊C4—48no—
210C4⋊Dic47—44no—
211Dic47⋊C4—28no—
212Dic47⋊C4—28no—
213C4×Dic47—28no—
214C4×Dic47—44no—
215C23×C47C22×D411yescharacteristic
216C23×C47C22×D411yescharacteristic
217C23×C47C22×D411yescharacteristic
218C23×C47C2×#4111yescharacteristic
219C23×C47C2×#4111yescharacteristic
220C23×C47C2×#4111yescharacteristic
221C23×C47C2×#4111yescharacteristic
222C23×C47C2×#4111yescharacteristic
223C23×C47C2×#4111yescharacteristic
224C23×C47C2×#4111yescharacteristic
225C23×C47C2×#4111yescharacteristic
226C23×C47H(5,𝔽2)11yescharacteristic
227C23×C47H(5,𝔽2)11yescharacteristic
228C23×C47H(5,𝔽2)11yescharacteristic
229C23×C472−1+411yescharacteristic
230C22×D47—24no—
231C22×D47—24no—
232C22×D47—24no—
233C22×D47—24no—
234C22×D47—24no—
235C22×D47—24no—
236C22×D47—24no—
237C22×D47—42no—
238C22×D47—42no—
239C22×D47—42no—
240C22×D47—42no—
241C22×D47—42no—
242C22×D47—42no—
243C22×D47—42no—
244C22×D47—42no—
245C22×D47—42no—
246C22×D47—42no—
247C22×D47—42no—
248C22×D47—42no—
249C22×D47—42no—
250C22×D47—42no—
251C22×D47—42no—
252C22×D47—42no—
253C22×D47—42no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47—42no—
257C22×D47—42no—
258C22×D47—42no—
259C22×D47—42no—
260C22×D47—42no—
261C22×D47—42no—
262C22×D47—42no—
263C22×D47—42no—
264C22×D47—42no—
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—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—42no—
280C2×C4×C47—42no—
281C2×C4×C47—42no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47#12114yes—
294C2×C4×C47#12314yes—
295C2×C4×C47#12314yes—
296C2×C4×C47#12314yes—
297C2×C4×C47#12414yes—
298C2×C4×C47#12614yes—
299C2×C4×C47#12614yes—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—41no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47#12114yes—
335D188—416no—
336#15147—471nomaximal, Sylow
337C22×C47C2×#12111yescharacteristic
338C22×C47C2×#12111yescharacteristic
339C22×C47C2×#12311yescharacteristic
340C22×C47C2×#12311yescharacteristic
341C22×C47C2×#12311yescharacteristic
342C22×C47#52511yescharacteristic
343C22×C47C2×#12411yescharacteristic
344C22×C47C2×#12611yescharacteristic
345C22×C47C2×#12611yescharacteristic
346C22×C47#52911yescharacteristic
347C22×C47#52911yescharacteristic
348C22×C47#53211yescharacteristic
349C22×C47#53211yescharacteristic
350C22×C47#53511yescharacteristic
351C22×C47#53711yescharacteristic
352C22×C47#54011yescharacteristic
353C22×C47#54011yescharacteristic
354C22×C47#54211yescharacteristic
355C22×C47#54211yescharacteristic
356C22×C47D4211yescharacteristic
357C22×C47#54611yescharacteristic
358C22×C47#54611yescharacteristic
359C22×C47#54711yescharacteristic
360C22×C47#54711yescharacteristic
361C22×C47#55011yescharacteristic
362C22×C47#55011yescharacteristic
363C22×C47#55311yescharacteristic
364C22×C47#55311yescharacteristic
365C22×C47#55511yescharacteristic
366C22×C47#55611yescharacteristic
367C22×C47#55611yescharacteristic
368C22×C47#55911yescharacteristic
369C22×C47#55911yescharacteristic
370C22×C47#55911yescharacteristic
371C22×C47#55911yescharacteristic
372C2×D47—44no—
373C2×D47—44no—
374C2×D47—44no—
375C2×D47—44no—
376C2×D47—44no—
377C2×D47—44no—
378C2×D47—44no—
379C2×D47—82no—
380C2×D47—82no—
381C2×D47—82no—
382C2×D47—82no—
383C2×D47—82no—
384C2×D47—82no—
385C2×D47—82no—
386C2×D47—82no—
387C4×C47—42no—
388C4×C47—42no—
389C4×C47—82no—
390C4×C47—82no—
391C4×C47#39718yescomplemented
392Dic47—24no—
393Dic47—42no—
394Dic47—42no—
395Dic47—42no—
396Dic47—82no—
397C2×#397—472no—
398C2×#390—471no—
399C2×#390—471no—
400C2×#390—471no—
401C2×C4×C4⋊C4—471no—
402#1440—472no—
403#1440—472no—
404#1439—472no—
405C4⋊#95—471no—
406C4⋊#95—471no—
407C4⋊#95D4711yescharacteristic, complemented
408C2×C47C2×#39711yescharacteristic
409C2×C47#244511yescharacteristic
410C2×C47#244511yescharacteristic
411C2×C47#244711yescharacteristic
412C2×C47#244711yescharacteristic
413C2×C47#251211yescharacteristic
414C2×C47#251211yescharacteristic
415C2×C47#251311yescharacteristic
416C2×C47#251311yescharacteristic
417C2×C47#253511yescharacteristic
418C2×C47#253711yescharacteristic
419C2×C47#254811yescharacteristic
420C2×C47#259211yescharacteristic
421C2×C47#262411yescharacteristic
422C2×C47#285411yescharacteristic
423D47—84no—
424C23×D4—471no—
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4—471no—
428C22×C4⋊C4C2×D4711yescharacteristic
429C22×C4⋊C4C2×D4711yescharacteristic
430C22×C22⋊C4—472no—
431C22×C22⋊C4—472no—
432C22×C22⋊C4—472no—
433C22×C22⋊C4—472no—
434C22×C22⋊C4—472no—
435C22×C22⋊C4—472no—
436C22×C42—471no—
437C22×C42—471no—
438C22×C42C2×D4711yescharacteristic
439#397—948no—
440#390—944no—
441#390—944no—
442#390—944no—
443C4×C4⋊C4—944no—
444C2×#95—472no—
445C2×#95—472no—
446C2×#95—471no—
447C2×#95—471no—
448C2×#95—472no—
449C2×#95—472no—
450C2×#95C2×D4712yes—
451C2×#95C2×D4712yes—
452C47#1514711yescharacteristic, complemented, Sylow
453C25—472no—
454C22×D4—474no—
455C22×D4—942no—
456C22×D4—942no—
457C22×D4—942no—
458C22×D4—942no—
459C22×D4—942no—
460C22×D4—942no—
461C23×C4—471no—
462C23×C4—471no—
463C23×C4—471no—
464C23×C4—471no—
465C23×C4—472no—
466C23×C4C22×D4712yes—
467C23×C4C22×D4712yes—
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470C23×C4C22×D4711yescharacteristic
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—942no—
479C2×C4⋊C4—942no—
480C2×C4⋊C4—942no—
481C2×C4⋊C4—942no—
482C2×C4⋊C4—942no—
483C2×C4⋊C4—942no—
484C2×C4⋊C4—942no—
485C2×C4⋊C4—942no—
486C2×C22⋊C4—944no—
487C2×C22⋊C4—944no—
488C2×C22⋊C4—944no—
489C2×C22⋊C4—944no—
490C2×C22⋊C4—944no—
491C2×C22⋊C4—944no—
492C2×C22⋊C4—944no—
493C2×C22⋊C4—944no—
494C2×C22⋊C4—944no—
495C2×C22⋊C4—944no—
496C2×C22⋊C4—944no—
497C2×C22⋊C4—944no—
498C2×C22⋊C4—1882no—
499C2×C22⋊C4—1882no—
500C2×C22⋊C4—1882no—
501C2×C22⋊C4—1882no—
502C2×C22⋊C4—1882no—
503C2×C22⋊C4—1882no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—22no—
507C2×C42—474no—
508C2×C42—942no—
509C2×C42—942no—
510C2×C42—942no—
511C2×C42—942no—
512C2×C42—942no—
513#95—24no—
514#95—42no—
515#95—942no—
516#95—942no—
517#95—944no—
518#95—944no—
519#95—1882no—
520#95—1882no—
521C24—474no—
522C24—942no—
523C24—942no—
524C24—942no—
525C24—942no—
526C24—942no—
527C24—942no—
528C24—942no—
529C24—942no—
530C24—942no—
531C24—942no—
532C24—942no—
533C24—942no—
534C24—942no—
535C24—942no—
536C24C23×D4711yescharacteristic
537C2×D4—948no—
538C2×D4—948no—
539C2×D4—948no—
540C2×D4—1884no—
541C2×D4—1884no—
542C2×D4—1884no—
543C2×D4—1884no—
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—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—472no—
571C22×C4—472no—
572C22×C4—472no—
573C22×C4—472no—
574C22×C4—472no—
575C22×C4—472no—
576C22×C4—941no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4#1062535012yes—
606C22×C4#1062535012yes—
607C22×C4#1062535012yes—
608C22×C4D4×D4712yes—
609C22×C4D4×D4712yes—
610C22×C4D4×D4712yes—
611C22×C4#1062535212yes—
612C22×C4#1062535412yes—
613C22×C4#1062535412yes—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—948no—
617C4⋊C4—948no—
618C4⋊C4—1884no—
619C22⋊C4—1888no—
620C22⋊C4—1888no—
621C22⋊C4—1888no—
622C22⋊C4—1888no—
623C22⋊C4—1888no—
624C22⋊C4—1888no—
625C42—44no—
626C42—948no—
627C42—1884no—
628C23—944no—
629C23—944no—
630C23—944no—
631C23—944no—
632C23—944no—
633C23—944no—
634C23—944no—
635C23—1882no—
636C23—1882no—
637C23—1882no—
638C23—1882no—
639C23—1882no—
640C23—1882no—
641C23—1882no—
642C23—1882no—
643C23—1882no—
644C23—1882no—
645C23—1882no—
646C23—1882no—
647C23—1882no—
648C23—1882no—
649C23—1882no—
650C23—1882no—
651C23—1882no—
652C23—1882no—
653C23—1882no—
654C23—1882no—
655C23—1882no—
656C23—1882no—
657C23—1882no—
658C23—1882no—
659C23—1882no—
660C23—1882no—
661C23—1882no—
662C23—1882no—
663C23C2×D4×D4711yescharacteristic
664C23C2×D4×D4711yescharacteristic
665C23C2×D4×D4711yescharacteristic
666C23#41×D4711yescharacteristic
667C23#41×D4711yescharacteristic
668C23C2×#1062535211yescharacteristic
669C23C2×#1062535011yescharacteristic
670C23C2×#1062535011yescharacteristic
671C23C2×#1062535011yescharacteristic
672C23C2×#1062535411yescharacteristic
673C23C2×#1062535411yescharacteristic
674C23#1309406911yescharacteristic
675C23#1309407011yescharacteristic
676C23#1309407011yescharacteristic
677C23#1309407211yescharacteristic
678D4—18816no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
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—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—474no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4—1882no—
728C2×C4—1882no—
729C2×C4—1882no—
730C2×C4—1881no—
731C2×C4—1881no—
732C2×C4—1881no—
733C2×C4—1881no—
734C2×C4—1881no—
735C2×C4—1881no—
736C2×C4—1881no—
737C2×C4—1881no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1881no—
741C2×C4—1881no—
742C2×C4#1309399714yes—
743C2×C4#1309400614yes—
744C2×C4#1309400914yes—
745C2×C4#1309400914yes—
746C2×C4#1309401014yes—
747C2×C4#1309401814yes—
748C2×C4#1309401914yes—
749C22—3762no—
750C22—3762no—
751C22—3762no—
752C22—3762no—
753C22—3762no—
754C22—3762no—
755C22—3762no—
756C22—3762no—
757C22—1884no—
758C22—1884no—
759C22—1884no—
760C22—1884no—
761C22—1884no—
762C22—1884no—
763C22—1884no—
764C22#121×D4711yescharacteristic
765C22C2×#1309399711yescharacteristic
766C22C2×#1309400611yescharacteristic
767C22C2×#1309400911yescharacteristic
768C22C2×#1309400911yescharacteristic
769C22#1568963611yescharacteristic
770C22C2×#1309401011yescharacteristic
771C22C2×#1309401811yescharacteristic
772C22C2×#1309401911yescharacteristic
773C22#1568965811yescharacteristic
774C22#1568966011yescharacteristic
775C22#1568967011yescharacteristic
776C22#1568967411yescharacteristic
777C22#1568968911yescharacteristic
778C22#1568970311yescharacteristic
779C22#1568972411yescharacteristic
780C22#1568972911yescharacteristic
781C22#1568974511yescharacteristic
782C22#1568974711yescharacteristic
783C22#1568975711yescharacteristic
784C22#1568976411yescharacteristic
785C22#1568977011yescharacteristic
786C22#1568977411yescharacteristic
787C22#1568977511yescharacteristic
788C22#1568979311yescharacteristic
789C22#1568979411yescharacteristic
790C22#1568981711yescharacteristic
791C22#1568982111yescharacteristic
792C22#1568983611yescharacteristic
793C22#1568984511yescharacteristic
794C22#1568984711yescharacteristic
795C22#1568985511yescharacteristic
796C22#1568985511yescharacteristic
797C22#1568985611yescharacteristic
798C22#1568985811yescharacteristic
799C4—42no—
800C4—42no—
801C4—82no—
802C4—82no—
803C4—944no—
804C4—3762no—
805C4—1882no—
806C4—1882no—
807C4—1882no—
808C4#1568905218yescomplemented
809C2—3764no—
810C2C2×#1568905211yescharacteristic
811C2#2024715411yescharacteristic
812C2#2024715511yescharacteristic
813C2#2024717611yescharacteristic
814C2#2024717711yescharacteristic
815C2#2024796811yescharacteristic
816C2#2024797011yescharacteristic
817C2#2024797911yescharacteristic
818C2#2024798111yescharacteristic
819C2#2024829111yescharacteristic
820C2#2024830311yescharacteristic
821C2#2024838911yescharacteristic
822C2#2024887511yescharacteristic
823C2#2024918211yescharacteristic
824C2#2025172111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, cosocleC24×C47C24
FittingC47×C4⋊#95C2
prime radicalC23×D188C22
hypercenterC4⋊#95D47
hypocenterC47#15147
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#15689052C2semidirect
5. C2×C4×Dic47⋊C4C2semidirect
6. #20241636C2semidirect
7. #20241636C2semidirect
8. #20241632C2semidirect
9. #20241617C2semidirect
10. #20241617C2semidirect
11. C47×C4⋊#95C2semidirect
61. C2×Dic47⋊C4D4semidirect
391. C4×C47#397semidirect
407. C4⋊#95D47semidirect
452. C47#15147semidirect
808. C4#15689052semidirect

Maximal subgroups

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

subgroupindex
C2×#156890522
C2×#156890252
C2×#156890242
C2×C4×Dic47⋊C42
#202416362
#202416322
#202416172
C47×C4⋊#952
#1514747