Finite Group Databasebeta

← #26137584

Subgroups — #26137584

Order 12032.

2470 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2C2×#15689023C212yesmaximal
3C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
4C2×#15688968C211yesmaximal, characteristic, complemented
5#20241626C211yesmaximal, characteristic, complemented
6#20241625C211yesmaximal, characteristic, complemented
7#20241624C211yesmaximal, characteristic, complemented
8Dic47⋊#95C212yesmaximal, complemented
9#20241610C212yesmaximal, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C47×#1437C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C23×C4×D47C2211yescharacteristic
15C2×(C22⋊D47)⋊C4—24no—
16C2×(C22⋊D47)⋊C4—24no—
17C2×(C22⋊D47)⋊C4C418yescomplemented
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2212yes—
20C22×C22⋊Dic47C2212yes—
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C22×(C2×D47)⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2212yes—
24C22×C4×Dic47C2212yes—
25C22×C4×Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27#15689023C4116yescomplemented
28C4×Dic47⋊C4—24no—
29#15688968—24no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C22×C22⋊C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2212yes—
38C22×C42×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2212yes—
41C24×D47C2311yescharacteristic
42C22×C22⋊D47—22no—
43C22×C22⋊D47—22no—
44C22×C22⋊D47—24no—
45C22×C22⋊D47C2×C418yes—
46C22×C22⋊D47C2×C414yes—
47C23×Dic47—22no—
48C23×Dic47—22no—
49C23×Dic47—42no—
50C23×Dic47—42no—
51C23×Dic47C2×C414yes—
52C23×Dic47C2312yes—
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2312yes—
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C22×C4×D47—22no—
58C22×C4×D47—22no—
59C22×C4×D47—42no—
60C22×C4×D47—42no—
61C22×C4×D47C2×C414yes—
62(C22⋊D47)⋊C4—232no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—22no—
65C2×Dic47⋊C4—22no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4C2×C414yes—
68C2×Dic47⋊C4C2×C418yescomplemented
69C2×C22⋊Dic47—42no—
70C2×C22⋊Dic47—42no—
71C2×C22⋊Dic47C2×C418yescomplemented
72C2×(C2×D47)⋊C4—22no—
73C2×(C2×D47)⋊C4—22no—
74C2×(C2×D47)⋊C4—42no—
75C2×(C2×D47)⋊C4—42no—
76C2×(C2×D47)⋊C4—42no—
77C2×(C2×D47)⋊C4—42no—
78C2×(C2×D47)⋊C4C2×C414yes—
79C2×(C2×D47)⋊C4C2×C418yescomplemented
80C2×(C2×D47)⋊C4C2×C418yescomplemented
81C2×C4×Dic47—24no—
82C2×C4×Dic47—24no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—42no—
85C2×C4×Dic47C2×C414yes—
86C2×C4×Dic47C2×C418yescomplemented
87C2×C4×Dic47D414yes—
88C2×C4×Dic47D414yes—
89C47⋊#95—22no—
90C47⋊#95—24no—
91C47⋊#95—24no—
92C47⋊#95—42no—
93C47⋊#95—42no—
94C47⋊#95—42no—
95C25×C47C2311yescharacteristic
96C23×C4×C47C2312yes—
97C23×C4×C47C2312yes—
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2311yescharacteristic
100C2×C22⋊C4×C47—22no—
101C2×C22⋊C4×C47—22no—
102C2×C22⋊C4×C47—42no—
103C2×C22⋊C4×C47—42no—
104C2×C22⋊C4×C47C2×C414yes—
105C2×C22⋊C4×C47C2×C418yescomplemented
106C2×C42×C47—22no—
107C2×C42×C47—42no—
108#95×C47—22no—
109#95×C47—42no—
110C24×C47—21no—
111C24×C47—21no—
112C24×C47—22no—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47C22×C412yes—
118C24×C47C22×C414yes—
119C24×C47C2411yescharacteristic
120C23×D47—21no—
121C23×D47—21no—
122C23×D47—22no—
123C23×D47—22no—
124C23×D47—22no—
125C23×D47—22no—
126C23×D47—22no—
127C23×D47C22×C412yes—
128C23×D47C22×C414yes—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
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×C47C22×C412yes—
148C22×C4×C47C22×C414yes—
149C22×C4×C47C22×C414yes—
150C22×C4×C47C22×C412yes—
151C22×C4×C47C2×D412yes—
152C22×C4×C47C2×D412yes—
153C2×C22⋊D47—28no—
154C2×C22⋊D47—28no—
155C2×C22⋊D47—216no—
156C2×C22⋊D47—216no—
157C2×C22⋊D47C42116yescomplemented
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—28no—
177C22×Dic47—48no—
178C22×Dic47—44no—
179C22×Dic47—48no—
180C22×Dic47—44no—
181C22×Dic47C22×C414yes—
182C22×Dic47C22×C412yes—
183C22×Dic47C22×C414yes—
184C22×Dic47C22×C412yes—
185C22×Dic47C22×C412yes—
186C22×Dic47C22×C414yes—
187C22×Dic47C2×D412yes—
188C22×Dic47C2×D412yes—
189C22×Dic47C2×D412yes—
190C22×Dic47C2×D412yes—
191C22×Dic47#4114yes—
192C2×C4×D47—28no—
193C2×C4×D47—48no—
194C2×C4×D47—44no—
195C2×C4×D47—48no—
196C2×C4×D47—44no—
197C22⋊C4×C47—28no—
198C22⋊C4×C47—48no—
199C42×C47—44no—
200C22⋊Dic47—48no—
201(C2×D47)⋊C4—28no—
202(C2×D47)⋊C4—48no—
203(C2×D47)⋊C4—48no—
204Dic47⋊C4—28no—
205Dic47⋊C4—216no—
206C4×Dic47—216no—
207C4×Dic47—44no—
208C4×Dic47C22⋊C4116yescomplemented
209C23×C47—22no—
210C23×C47—22no—
211C23×C47—24no—
212C23×C47—24no—
213C23×C47—24no—
214C23×C47—24no—
215C23×C47—24no—
216C23×C47—24no—
217C23×C47—24no—
218C23×C47—24no—
219C23×C47—41no—
220C23×C47—42no—
221C23×C47—41no—
222C23×C47—41no—
223C23×C47—41no—
224C23×C47—42no—
225C23×C47—42no—
226C23×C47—42no—
227C23×C47—42no—
228C23×C47—42no—
229C23×C47C2×C4214yes—
230C23×C47C23×C411yescharacteristic
231C23×C47C23×C412yes—
232C23×C47C22×D411yescharacteristic
233C23×C47C22×D411yescharacteristic
234C23×C47C2×#4112yes—
235C23×C47H(5,𝔽2)12yes—
236C23×C47H(5,𝔽2)12yes—
237C23×C47H(5,𝔽2)12yes—
238C23×C472−1+412yes—
239C22×D47—22no—
240C22×D47—22no—
241C22×D47—24no—
242C22×D47—24no—
243C22×D47—24no—
244C22×D47—24no—
245C22×D47—24no—
246C22×D47—24no—
247C22×D47—24no—
248C22×D47—24no—
249C22×D47—41no—
250C22×D47—42no—
251C22×D47—41no—
252C22×D47—41no—
253C22×D47—41no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47—42no—
257C22×D47—42no—
258C22×D47—42no—
259C22×D47C2×C4214yes—
260C2×C4×C47—24no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—24no—
264C2×C4×C47—22no—
265C2×C4×C47—24no—
266C2×C4×C47—24no—
267C2×C4×C47—24no—
268C2×C4×C47—24no—
269C2×C4×C47—24no—
270C2×C4×C47—24no—
271C2×C4×C47—24no—
272C2×C4×C47—42no—
273C2×C4×C47—41no—
274C2×C4×C47—42no—
275C2×C4×C47—41no—
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47—42no—
281C2×C4×C47—42no—
282C2×C4×C47—42no—
283C2×C4×C47C2×C22⋊C414yes—
284C22⋊D47—232no—
285C2×Dic47—24no—
286C2×Dic47—22no—
287C2×Dic47—24no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—24no—
291C2×Dic47—24no—
292C2×Dic47—24no—
293C2×Dic47—24no—
294C2×Dic47—24no—
295C2×Dic47—24no—
296C2×Dic47—24no—
297C2×Dic47—416no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301C2×Dic47—41no—
302C2×Dic47—42no—
303C2×Dic47—41no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47C2×C4214yes—
310C2×Dic47C2×C22⋊C414yes—
311C2×Dic47C2×C22⋊C414yes—
312C2×Dic47#11714yes—
313C2×Dic47C4×D418yes—
314C2×Dic47C4×D418yes—
315C4×D47—416no—
316#13785—471nomaximal, Sylow
317C22×C47—24no—
318C22×C47—28no—
319C22×C47—42no—
320C22×C47—42no—
321C22×C47—44no—
322C22×C47—44no—
323C22×C47—44no—
324C22×C47—44no—
325C22×C47—44no—
326C22×C47C22×C4211yescharacteristic
327C22×C47C22×C22⋊C411yescharacteristic
328C22×C47C2×#11711yescharacteristic
329C22×C47C2×C4×D412yes—
330C22×C47C2×C4×D412yes—
331C22×C47#51812yes—
332C22×C47#51812yes—
333C22×C47#51812yes—
334C22×C47#52012yes—
335C22×C47#52012yes—
336C22×C47#52012yes—
337C22×C47#53511yescharacteristic
338C22×C47#53511yescharacteristic
339C22×C47#53512yes—
340C22×C47#53511yescharacteristic
341C22×C47#53611yescharacteristic
342C22×C47#53712yes—
343C22×C47#54012yes—
344C22×C47#54012yes—
345C22×C47#54212yes—
346C22×C47#54212yes—
347C2×D47—24no—
348C2×D47—28no—
349C2×D47—42no—
350C2×D47—42no—
351C2×D47—44no—
352C2×D47—44no—
353C2×D47—44no—
354C2×D47—44no—
355C2×D47—44no—
356C4×C47—24no—
357C4×C47—42no—
358C4×C47—44no—
359C4×C47—44no—
360Dic47—24no—
361Dic47—42no—
362Dic47—44no—
363Dic47—44no—
364Dic47C4×C22⋊C418yes—
365C22×C4×D4—471no—
366C2×#390—472no—
367C2×C4×C4⋊C4—471no—
368C2×#376—471no—
369#1437—471no—
370#1437—471no—
371#1437—471no—
372#1437D4711yescharacteristic, complemented
373C4⋊#95—472no—
374C22⋊#95—472no—
375C22⋊#95—472no—
376C2×C47—44no—
377C2×C47C2×C4×C22⋊C411yescharacteristic
378C2×C47#227512yes—
379C2×C47#230911yescharacteristic
380C2×C47#231111yescharacteristic
381C2×C47#231912yes—
382C2×C47#232412yes—
383C2×C47#232412yes—
384C2×C47#232612yes—
385C2×C47#232812yes—
386D47—44no—
387C23×D4—471no—
388C24×C4—471no—
389C24×C4—471no—
390C2×C4×D4—478no—
391C2×C4×D4—944no—
392C2×C4×D4—944no—
393C22×C4⋊C4—471no—
394C22×C4⋊C4—472no—
395C22×C22⋊C4—471no—
396C22×C22⋊C4—472no—
397C22×C22⋊C4—472no—
398C22×C22⋊C4—472no—
399C22×C22⋊C4C2×D4711yescharacteristic
400C22×C22⋊C4C2×D4712yes—
401C22×C42—471no—
402C22×C42—472no—
403C22×C42—471no—
404C22×C42C2×D4711yescharacteristic
405#390—4716no—
406C4×C4⋊C4—944no—
407#376—944no—
408C2×#95—472no—
409C2×#95—472no—
410C2×#95—471no—
411C2×#95—472no—
412C2×#95—472no—
413C2×#95—472no—
414C2×#95C2×D4711yescharacteristic
415C2×#95C2×D4712yes—
416C47#1378511yescharacteristic, complemented, Sylow
417C25—471no—
418C25C22×D4711yescharacteristic
419C22×D4—474no—
420C22×D4—478no—
421C22×D4—942no—
422C22×D4—942no—
423C22×D4—944no—
424C23×C4—471no—
425C23×C4—471no—
426C23×C4—472no—
427C23×C4—472no—
428C23×C4—471no—
429C23×C4—474no—
430C23×C4—474no—
431C23×C4—942no—
432C23×C4—942no—
433C23×C4—942no—
434C23×C4—942no—
435C23×C4—1882no—
436C23×C4—1882no—
437C23×C4—1882no—
438C23×C4—1882no—
439C23×C4C22×D4712yes—
440C23×C4C22×D4712yes—
441C23×C4C22×D4711yescharacteristic
442C23×C4C22×D4711yescharacteristic
443C4×D4—9432no—
444C2×C4⋊C4—474no—
445C2×C4⋊C4—478no—
446C2×C4⋊C4—942no—
447C2×C4⋊C4—942no—
448C2×C4⋊C4—944no—
449C2×C4⋊C4—944no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—474no—
455C2×C22⋊C4—478no—
456C2×C22⋊C4—478no—
457C2×C22⋊C4—478no—
458C2×C22⋊C4—942no—
459C2×C22⋊C4—942no—
460C2×C22⋊C4—1882no—
461C2×C22⋊C4—1882no—
462C2×C22⋊C4—1882no—
463C2×C22⋊C4—1882no—
464C2×C22⋊C4—1882no—
465C2×C22⋊C4—1882no—
466C2×C22⋊C4C4×D4714yes—
467C2×C22⋊C4C4×D4718yescomplemented
468C2×C42—22no—
469C2×C42—42no—
470C2×C42—474no—
471C2×C42—474no—
472C2×C42—474no—
473C2×C42—478no—
474C2×C42—944no—
475C2×C42—944no—
476C2×C42—942no—
477C2×C42—1882no—
478#95—22no—
479#95—42no—
480#95—944no—
481#95—944no—
482#95—942no—
483#95—1882no—
484#95—1882no—
485#95—1882no—
486C24—21no—
487C24—21no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—474no—
494C24—472no—
495C24—941no—
496C24—941no—
497C24—942no—
498C24—942no—
499C24—942no—
500C24—942no—
501C24—942no—
502C24C2×C4×D4714yes—
503C24C2×C4×D4712yes—
504C24C23×D4711yescharacteristic
505C2×D4—4716no—
506C2×D4—948no—
507C2×D4—948no—
508C2×D4—9416no—
509C2×D4—9416no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—472no—
529C22×C4—474no—
530C22×C4—472no—
531C22×C4—472no—
532C22×C4—474no—
533C22×C4—472no—
534C22×C4—472no—
535C22×C4—472no—
536C22×C4—474no—
537C22×C4—474no—
538C22×C4—472no—
539C22×C4—948no—
540C22×C4—948no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—941no—
546C22×C4—941no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—942no—
558C22×C4—942no—
559C22×C4—1888no—
560C22×C4—1884no—
561C22×C4—1888no—
562C22×C4—1884no—
563C22×C4—1888no—
564C22×C4—1884no—
565C22×C4—1888no—
566C22×C4—1884no—
567C22×C4C2×C4×D4714yes—
568C22×C4C2×C4×D4714yes—
569C22×C4C2×C4×D4712yes—
570C22×C4C2×C4×D4712yes—
571C22×C4D4×D4712yes—
572C22×C4D4×D4712yes—
573C4⋊C4—9416no—
574C4⋊C4—948no—
575C22⋊C4—28no—
576C22⋊C4—48no—
577C22⋊C4—948no—
578C22⋊C4—1888no—
579C22⋊C4—1888no—
580C22⋊C4—1888no—
581C42—44no—
582C42—4716no—
583C42—9416no—
584C42—1884no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—42no—
596C23—42no—
597C23—41no—
598C23—41no—
599C23—42no—
600C23—41no—
601C23—41no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—474no—
606C23—942no—
607C23—942no—
608C23—944no—
609C23—944no—
610C23—944no—
611C23—944no—
612C23—944no—
613C23—944no—
614C23—944no—
615C23—944no—
616C23—1882no—
617C23—1882no—
618C23—1881no—
619C23—1881no—
620C23—1882no—
621C23—1881no—
622C23—1881no—
623C23—1882no—
624C23—1882no—
625C23—1882no—
626C23C42×D4714yes—
627C23C22×C4×D4711yescharacteristic
628C23C22×C4×D4712yes—
629C23C2×D4×D4711yescharacteristic
630C23C2×D4×D4711yescharacteristic
631C23#41×D4712yes—
632C23#1309406912yes—
633C23#1309406912yes—
634C23#1309407012yes—
635C23#1309407112yes—
636D4—9432no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—474no—
661C2×C4—474no—
662C2×C4—474no—
663C2×C4—478no—
664C2×C4—478no—
665C2×C4—474no—
666C2×C4—944no—
667C2×C4—942no—
668C2×C4—944no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—944no—
672C2×C4—944no—
673C2×C4—944no—
674C2×C4—944no—
675C2×C4—944no—
676C2×C4—944no—
677C2×C4—944no—
678C2×C4—18816no—
679C2×C4—18816no—
680C2×C4—1882no—
681C2×C4—1881no—
682C2×C4—1882no—
683C2×C4—1882no—
684C2×C4—1882no—
685C2×C4—1882no—
686C2×C4—1881no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4—1882no—
691C2×C4C22⋊C4×D4714yes—
692C22—24no—
693C22—28no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—44no—
698C22—44no—
699C22—42no—
700C22—42no—
701C22—944no—
702C22—948no—
703C22—1884no—
704C22—1884no—
705C22—1884no—
706C22—1884no—
707C22—1884no—
708C22—1882no—
709C22—1882no—
710C22C2×C42×D4711yescharacteristic
711C22C2×C22⋊C4×D4711yescharacteristic
712C22#117×D4711yescharacteristic
713C22C4×D4×D4712yes—
714C22C4×D4×D4712yes—
715C22#1568959512yes—
716C22#1568959512yes—
717C22#1568959612yes—
718C22#1568960212yes—
719C22#1568960212yes—
720C22#1568960312yes—
721C22#1568968611yescharacteristic
722C22#1568968811yescharacteristic
723C22#1568968912yes—
724C22#1568969111yescharacteristic
725C22#1568969511yescharacteristic
726C22#1568970012yes—
727C22#1568972312yes—
728C22#1568972512yes—
729C22#1568973712yes—
730C22#1568973912yes—
731C4—24no—
732C4—44no—
733C4—44no—
734C4—42no—
735C4—478no—
736C4—944no—
737C4—1884no—
738C4—1884no—
739C4—1882no—
740C2—44no—
741C2—1884no—
742C2C4×C22⋊C4×D4711yescharacteristic
743C2#2024574712yes—
744C2#2024596711yescharacteristic
745C2#2024597511yescharacteristic
746C2#2024602912yes—
747C2#2024607412yes—
748C2#2024607612yes—
749C2#2024609712yes—
750C2#2024610912yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×#1437C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenter#1437D47
hypocenterC47#13785
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic47⋊C4C2semidirect
4. C2×#15688968C2semidirect
5. #20241626C2semidirect
6. #20241625C2semidirect
7. #20241624C2semidirect
8. Dic47⋊#95C2semidirect
9. #20241610C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C47×#1437C2semidirect
17. C2×(C22⋊D47)⋊C4C4semidirect
27. #15689023C4semidirect
68. C2×Dic47⋊C4C2×C4semidirect
71. C2×C22⋊Dic47C2×C4semidirect
79. C2×(C2×D47)⋊C4C2×C4semidirect
80. C2×(C2×D47)⋊C4C2×C4semidirect
86. C2×C4×Dic47C2×C4semidirect
105. C2×C22⋊C4×C47C2×C4semidirect
157. C2×C22⋊D47C42semidirect
208. C4×Dic47C22⋊C4semidirect
372. #1437D47semidirect
416. C47#13785semidirect
467. C2×C22⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D47)⋊C42
C2×#156890232
C2×C4×Dic47⋊C42
C2×#156889682
#202416262
#202416252
#202416242
Dic47⋊#952
#202416102
(C2×D47)⋊#952
C47×#14372
#1378547