Finite Group Databasebeta

← #26137578

Subgroups — #26137578

Order 12032.

2686 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093986C211yesmaximal, characteristic
2C2×#15689001C212yesmaximal
3C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
4C2×#95×D47C211yesmaximal, characteristic, complemented
5#20241626C211yesmaximal, characteristic, complemented
6#20241624C211yesmaximal, characteristic, complemented
7#20241620C211yesmaximal, characteristic, complemented
8#20241613C212yesmaximal, complemented
9(C2×D47)⋊#95C212yesmaximal, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C47×#1436C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C23×C4×D47C2212yes—
14C23×C4×D47C2211yescharacteristic
15C23×C4×D47C2211yescharacteristic
16C2×#13093986—24no—
17C2×#13093986—24no—
18C2×#13093986C418yescomplemented
19C22×(C2×D47)⋊C4C2211yescharacteristic
20C22×(C2×D47)⋊C4C2212yes—
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C22×(C2×D47)⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2212yes—
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26#15689001C4116yescomplemented
27C4×(C2×D47)⋊C4—24no—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35#95×D47—24no—
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2212yes—
40C2×#95×C47C2212yes—
41C24×D47C2311yescharacteristic
42C24×D47C2311yescharacteristic
43C22×D188—22no—
44C22×D188—22no—
45C22×D188—24no—
46C22×D188C2×C418yes—
47C22×D188C2×C414yes—
48C23×Dic47C2312yes—
49C23×Dic47C2312yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C22×C4×D47—24no—
53C22×C4×D47—24no—
54C22×C4×D47—22no—
55C22×C4×D47—22no—
56C22×C4×D47—42no—
57C22×C4×D47—42no—
58C22×C4×D47—42no—
59C22×C4×D47—42no—
60C22×C4×D47—42no—
61C22×C4×D47—42no—
62C22×C4×D47—42no—
63C22×C4×D47—42no—
64C22×C4×D47C2×C414yes—
65C22×C4×D47C2×C418yescomplemented
66C22×C4×D47C2×C414yescomplemented
67C22×C4×D47D414yes—
68C22×C4×D47D414yes—
69#13093986—232no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—22no—
72C2×(C2×D47)⋊C4—22no—
73C2×(C2×D47)⋊C4—24no—
74C2×(C2×D47)⋊C4—22no—
75C2×(C2×D47)⋊C4—22no—
76C2×(C2×D47)⋊C4—42no—
77C2×(C2×D47)⋊C4—42no—
78C2×(C2×D47)⋊C4—42no—
79C2×(C2×D47)⋊C4—42no—
80C2×(C2×D47)⋊C4C2×C414yes—
81C2×(C2×D47)⋊C4C2×C418yescomplemented
82C2×(C2×D47)⋊C4C2×C414yescomplemented
83C2×(C2×D47)⋊C4C2×C418yescomplemented
84C2×(C2×D47)⋊C4C2×C418yescomplemented
85C2×C4×Dic47—22no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47—22no—
88C2×C4×Dic47—42no—
89C2×C4×Dic47C2×C414yescomplemented
90C47⋊#95—22no—
91C47⋊#95—24no—
92C47⋊#95—24no—
93C47⋊#95—42no—
94C47⋊#95—42no—
95C47⋊#95—42no—
96C47⋊#95C2×C418yescomplemented
97C23×C4×C47C2312yes—
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2312yes—
100C23×C4×C47C2311yescharacteristic
101C23×C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47C2×C414yescomplemented
105C2×C42×C47—22no—
106C2×C42×C47—42no—
107#95×C47—22no—
108#95×C47—42no—
109#95×C47C2×C418yescomplemented
110C24×C47C2411yescharacteristic
111C23×D47—22no—
112C23×D47—22no—
113C23×D47—22no—
114C23×D47—22no—
115C23×D47—21no—
116C23×D47—21no—
117C23×D47—22no—
118C23×D47—22no—
119C23×D47—22no—
120C23×D47—22no—
121C23×D47—22no—
122C23×D47C22×C414yes—
123C23×D47C22×C412yes—
124C23×D47C22×C412yes—
125C23×D47C22×C414yes—
126C23×D47C2×D412yes—
127C23×D47C2×D412yes—
128C23×D47#4114yes—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
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×C47C22×C412yes—
151C22×C4×C47C22×C414yes—
152C22×C4×C47C22×C414yes—
153C22×C4×C47C22×C412yes—
154C22×C4×C47C22×C414yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D412yes—
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×Dic47C22×C414yes—
177C22×Dic47C22×C414yes—
178C22×Dic47C22×C412yes—
179C22×Dic47C22×C412yes—
180C22×Dic47C2×D412yes—
181C22×Dic47C2×D412yes—
182C2×D188—28no—
183C2×D188—28no—
184C2×D188—216no—
185C2×D188—216no—
186C2×D188C42116yescomplemented
187C2×C4×D47—216no—
188C2×C4×D47—28no—
189C2×C4×D47—48no—
190C2×C4×D47—48no—
191C2×C4×D47—48no—
192C2×C4×D47—48no—
193C2×C4×D47—44no—
194C2×C4×D47—44no—
195C2×C4×D47—48no—
196C2×C4×D47—48no—
197C2×C4×D47—44no—
198C2×C4×D47—44no—
199C2×C4×D47—48no—
200C2×C4×D47—48no—
201C2×C4×D47—48no—
202C2×C4×D47—48no—
203C2×C4×D47C22⋊C4116yescomplemented
204C4⋊C4×C47—28no—
205C42×C47—44no—
206(C2×D47)⋊C4—28no—
207(C2×D47)⋊C4—216no—
208(C2×D47)⋊C4—28no—
209(C2×D47)⋊C4—48no—
210(C2×D47)⋊C4—48no—
211C4×Dic47—28no—
212C4×Dic47—44no—
213C23×C47C23×C411yescharacteristic
214C23×C47C23×C412yes—
215C23×C47C22×D411yescharacteristic
216C23×C47C22×D411yescharacteristic
217C23×C47C2×#4112yes—
218C23×C47H(5,𝔽2)12yes—
219C23×C47H(5,𝔽2)12yes—
220C23×C47H(5,𝔽2)12yes—
221C23×C472−1+412yes—
222C22×D47—24no—
223C22×D47—24no—
224C22×D47—24no—
225C22×D47—24no—
226C22×D47—24no—
227C22×D47—24no—
228C22×D47—24no—
229C22×D47—22no—
230C22×D47—22no—
231C22×D47—22no—
232C22×D47—22no—
233C22×D47—24no—
234C22×D47—24no—
235C22×D47—24no—
236C22×D47—24no—
237C22×D47—24no—
238C22×D47—22no—
239C22×D47—22no—
240C22×D47—24no—
241C22×D47—24no—
242C22×D47—24no—
243C22×D47—24no—
244C22×D47—24no—
245C22×D47—24no—
246C22×D47—24no—
247C22×D47—24no—
248C22×D47—42no—
249C22×D47—41no—
250C22×D47—41no—
251C22×D47—41no—
252C22×D47—41no—
253C22×D47—42no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47—42no—
257C22×D47—42no—
258C22×D47C2×C4214yes—
259C22×D47C2×C4214yes—
260C22×D47C2×C22⋊C414yes—
261C22×D47#11714yes—
262C22×D47C4×D418yes—
263C22×D47C4×D418yes—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—24no—
267C2×C4×C47—24no—
268C2×C4×C47—24no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—24no—
272C2×C4×C47—22no—
273C2×C4×C47—24no—
274C2×C4×C47—24no—
275C2×C4×C47—24no—
276C2×C4×C47—24no—
277C2×C4×C47—24no—
278C2×C4×C47—24no—
279C2×C4×C47—24no—
280C2×C4×C47—42no—
281C2×C4×C47—42no—
282C2×C4×C47—42no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
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×C47C2×C4214yes—
292C2×C4×C47C2×C22⋊C414yes—
293C2×Dic47—24no—
294C2×Dic47—24no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—24no—
299C2×Dic47—24no—
300C2×Dic47—24no—
301C2×Dic47—24no—
302C2×Dic47—24no—
303C2×Dic47—24no—
304C2×Dic47—24no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47C2×C22⋊C414yes—
317D188—232no—
318C4×D47—416no—
319C4×D47—416no—
320C4×D47—432no—
321#13784—471nomaximal, Sylow
322C22×C47C22×C4211yescharacteristic
323C22×C47C22×C22⋊C411yescharacteristic
324C22×C47C2×#11711yescharacteristic
325C22×C47C2×C4×D412yes—
326C22×C47C2×C4×D412yes—
327C22×C47#51812yes—
328C22×C47#51812yes—
329C22×C47#51812yes—
330C22×C47#52012yes—
331C22×C47#52012yes—
332C22×C47#52012yes—
333C22×C47#53412yes—
334C22×C47#53411yescharacteristic
335C22×C47#53411yescharacteristic
336C22×C47#53511yescharacteristic
337C22×C47#53611yescharacteristic
338C22×C47#53712yes—
339C22×C47#53812yes—
340C22×C47#53812yes—
341C22×C47#53912yes—
342C22×C47#53912yes—
343C2×D47—24no—
344C2×D47—24no—
345C2×D47—28no—
346C2×D47—28no—
347C2×D47—28no—
348C2×D47—28no—
349C2×D47—28no—
350C2×D47—28no—
351C2×D47—24no—
352C2×D47—28no—
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—44no—
356C2×D47—44no—
357C2×D47—44no—
358C2×D47—44no—
359C2×D47—44no—
360C2×D47C4×C22⋊C418yes—
361C4×C47—24no—
362C4×C47—24no—
363C4×C47—42no—
364C4×C47—44no—
365C4×C47—44no—
366Dic47—24no—
367Dic47—42no—
368Dic47—44no—
369Dic47—44no—
370C22×C4×D4—471no—
371C2×#386—472no—
372C2×C4×C22⋊C4—471no—
373C22×#95—471no—
374#1437—471no—
375#1437—471no—
376#1436—471no—
377#1436D4711yescharacteristic, complemented
378#1434—472no—
379C22⋊#95—472no—
380C22⋊#95—472no—
381C2×C47C2×C4×C22⋊C411yescharacteristic
382C2×C47#227512yes—
383C2×C47#230811yescharacteristic
384C2×C47#231111yescharacteristic
385C2×C47#231812yes—
386C2×C47#232112yes—
387C2×C47#232212yes—
388C2×C47#232512yes—
389C2×C47#232512yes—
390D47—28no—
391D47—44no—
392C23×D4—471no—
393C24×C4—471no—
394C24×C4—471no—
395C24×C4—472no—
396C2×C4×D4—478no—
397C2×C4×D4—944no—
398C2×C4×D4—944no—
399C22×C4⋊C4C2×D4711yescharacteristic
400C22×C22⋊C4—471no—
401C22×C22⋊C4—471no—
402C22×C22⋊C4—472no—
403C22×C22⋊C4—472no—
404C22×C22⋊C4—472no—
405C22×C42—471no—
406C22×C42—471no—
407C22×C42C2×D4711yescharacteristic
408#386—4716no—
409C4×C22⋊C4—944no—
410C2×#95—472no—
411C2×#95—472no—
412C2×#95—472no—
413C2×#95—471no—
414C2×#95—472no—
415C2×#95—472no—
416C2×#95—472no—
417C2×#95—944no—
418C2×#95C2×D4711yescharacteristic
419C2×#95C2×D4712yes—
420C2×#95C2×D4712yes—
421C47#1378411yescharacteristic, complemented, Sylow
422C25—471no—
423C25—471no—
424C22×D4—474no—
425C22×D4—478no—
426C22×D4—942no—
427C22×D4—942no—
428C22×D4—944no—
429C23×C4—471no—
430C23×C4—474no—
431C23×C4—474no—
432C23×C4—474no—
433C23×C4—472no—
434C23×C4—471no—
435C23×C4—472no—
436C23×C4—474no—
437C23×C4—478no—
438C23×C4—942no—
439C23×C4—942no—
440C23×C4—944no—
441C23×C4—944no—
442C23×C4—1882no—
443C23×C4—1882no—
444C23×C4—1882no—
445C23×C4—1882no—
446C23×C4—1882no—
447C23×C4—1882no—
448C23×C4—1882no—
449C23×C4—1882no—
450C23×C4C22×D4712yes—
451C23×C4C22×D4711yescharacteristic
452C23×C4C22×D4712yes—
453C23×C4C22×D4711yescharacteristic
454C23×C4C22×D4711yescharacteristic
455C4×D4—9432no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4C4×D4714yescomplemented
459C2×C22⋊C4—474no—
460C2×C22⋊C4—474no—
461C2×C22⋊C4—478no—
462C2×C22⋊C4—478no—
463C2×C22⋊C4—478no—
464C2×C22⋊C4—942no—
465C2×C22⋊C4—942no—
466C2×C22⋊C4—944no—
467C2×C22⋊C4—944no—
468C2×C22⋊C4—942no—
469C2×C22⋊C4—942no—
470C2×C22⋊C4—1882no—
471C2×C22⋊C4—1882no—
472C2×C22⋊C4—1882no—
473C2×C22⋊C4—1882no—
474C2×C42—22no—
475C2×C42—42no—
476C2×C42—474no—
477C2×C42—942no—
478C2×C42—942no—
479C2×C42—942no—
480C2×C42—1882no—
481#95—22no—
482#95—42no—
483#95—478no—
484#95—944no—
485#95—944no—
486#95—942no—
487#95—1882no—
488#95—1882no—
489#95—1882no—
490#95C4×D4718yescomplemented
491C24—472no—
492C24—474no—
493C24—472no—
494C24—472no—
495C24—474no—
496C24—474no—
497C24—472no—
498C24—942no—
499C24—942no—
500C24—942no—
501C24—942no—
502C24—941no—
503C24—941no—
504C24—942no—
505C24—942no—
506C24—942no—
507C24—942no—
508C24—942no—
509C24C23×D4711yescharacteristic
510C2×D4—4716no—
511C2×D4—948no—
512C2×D4—948no—
513C2×D4—9416no—
514C2×D4—9416no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—472no—
537C22×C4—472no—
538C22×C4—472no—
539C22×C4—4716no—
540C22×C4—474no—
541C22×C4—474no—
542C22×C4—472no—
543C22×C4—948no—
544C22×C4—9416no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—941no—
550C22×C4—941no—
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—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—1888no—
564C22×C4—1888no—
565C22×C4—1884no—
566C22×C4—1884no—
567C22×C4—1888no—
568C22×C4—1888no—
569C22×C4—1888no—
570C22×C4—1888no—
571C22×C4—1884no—
572C22×C4—1884no—
573C22×C4—1888no—
574C22×C4—1888no—
575C22×C4—1888no—
576C22×C4—1888no—
577C22×C4C2×C4×D4714yes—
578C22×C4C2×C4×D4714yes—
579C22×C4C2×C4×D4712yes—
580C22×C4C2×C4×D4714yes—
581C22×C4C2×C4×D4712yes—
582C22×C4C2×C4×D4712yes—
583C22×C4D4×D4712yes—
584C22×C4D4×D4712yes—
585C4⋊C4—28no—
586C22⋊C4—9416no—
587C22⋊C4—948no—
588C22⋊C4—948no—
589C22⋊C4—1888no—
590C22⋊C4—1888no—
591C42—44no—
592C42—948no—
593C42—1884no—
594C23—474no—
595C23—474no—
596C23—474no—
597C23—478no—
598C23—478no—
599C23—474no—
600C23—944no—
601C23—944no—
602C23—944no—
603C23—944no—
604C23—944no—
605C23—944no—
606C23—944no—
607C23—942no—
608C23—942no—
609C23—942no—
610C23—942no—
611C23—944no—
612C23—944no—
613C23—944no—
614C23—944no—
615C23—944no—
616C23—942no—
617C23—942no—
618C23—944no—
619C23—944no—
620C23—944no—
621C23—944no—
622C23—944no—
623C23—944no—
624C23—944no—
625C23—944no—
626C23—1882no—
627C23—1881no—
628C23—1881no—
629C23—1881no—
630C23—1881no—
631C23—1882no—
632C23—1882no—
633C23—1882no—
634C23—1882no—
635C23—1882no—
636C23C22×C4×D4711yescharacteristic
637C23C22×C4×D4712yes—
638C23C2×D4×D4711yescharacteristic
639C23C2×D4×D4711yescharacteristic
640C23#41×D4712yes—
641C23#1309406912yes—
642C23#1309407012yes—
643C23#1309407012yes—
644C23#1309407212yes—
645D4—9432no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—474no—
674C2×C4—944no—
675C2×C4—944no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—944no—
680C2×C4—944no—
681C2×C4—944no—
682C2×C4—944no—
683C2×C4—944no—
684C2×C4—944no—
685C2×C4—944no—
686C2×C4—18816no—
687C2×C4—18816no—
688C2×C4—18832no—
689C2×C4—1882no—
690C2×C4—1882no—
691C2×C4—1881no—
692C2×C4—1882no—
693C2×C4—1881no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4—1882no—
697C2×C4—1882no—
698C2×C4—1882no—
699C2×C4—1882no—
700C2×C4C42×D4714yes—
701C2×C4C22⋊C4×D4714yes—
702C22—478no—
703C22—948no—
704C22—948no—
705C22—948no—
706C22—948no—
707C22—948no—
708C22—944no—
709C22—944no—
710C22—948no—
711C22—944no—
712C22—948no—
713C22—1884no—
714C22—1884no—
715C22—1884no—
716C22—1884no—
717C22—1884no—
718C22—1882no—
719C22—1882no—
720C22C2×C42×D4711yescharacteristic
721C22C2×C22⋊C4×D4711yescharacteristic
722C22#117×D4711yescharacteristic
723C22C4×D4×D4712yes—
724C22C4×D4×D4712yes—
725C22#1568959512yes—
726C22#1568959512yes—
727C22#1568959712yes—
728C22#1568960412yes—
729C22#1568960512yes—
730C22#1568960512yes—
731C22#1568968112yes—
732C22#1568968311yescharacteristic
733C22#1568968411yescharacteristic
734C22#1568969111yescharacteristic
735C22#1568969811yescharacteristic
736C22#1568970312yes—
737C22#1568970912yes—
738C22#1568971212yes—
739C22#1568971912yes—
740C22#1568972112yes—
741C4—24no—
742C4—24no—
743C4—44no—
744C4—44no—
745C4—42no—
746C4—944no—
747C4—1884no—
748C4—1884no—
749C4—1882no—
750C2—948no—
751C2—1884no—
752C2C4×C22⋊C4×D4711yescharacteristic
753C2#2024574812yes—
754C2#2024596211yescharacteristic
755C2#2024597911yescharacteristic
756C2#2024602012yes—
757C2#2024604112yes—
758C2#2024605212yes—
759C2#2024608512yes—
760C2#2024608712yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×#1436C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenter#1436D47
hypocenterC47#13784
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D47)⋊C4C2semidirect
4. C2×#95×D47C2semidirect
5. #20241626C2semidirect
6. #20241624C2semidirect
7. #20241620C2semidirect
8. #20241613C2semidirect
9. (C2×D47)⋊#95C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C47×#1436C2semidirect
18. C2×#13093986C4semidirect
26. #15689001C4semidirect
65. C22×C4×D47C2×C4semidirect
66. C22×C4×D47C2×C4semidirect
81. C2×(C2×D47)⋊C4C2×C4semidirect
82. C2×(C2×D47)⋊C4C2×C4semidirect
83. C2×(C2×D47)⋊C4C2×C4semidirect
84. C2×(C2×D47)⋊C4C2×C4semidirect
89. C2×C4×Dic47C2×C4semidirect
96. C47⋊#95C2×C4semidirect
104. C2×C4⋊C4×C47C2×C4semidirect
109. #95×C47C2×C4semidirect
186. C2×D188C42semidirect
203. C2×C4×D47C22⋊C4semidirect
377. #1436D47semidirect
421. C47#13784semidirect
458. C2×C4⋊C4C4×D47semidirect
490. #95C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130939862
C2×#156890012
C2×C4×(C2×D47)⋊C42
C2×#95×D472
#202416262
#202416242
#202416202
#202416132
(C2×D47)⋊#952
C47×#14362
#1378447