Finite Group Databasebeta

← #26376699

Subgroups — #26376699

Order 12032.

2634 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094001C211yesmaximal, characteristic
2#20246466C214yesmaximal, complemented
3#20246394C214yesmaximal, complemented
4#20246266C212yesmaximal, complemented
5#20246266C212yesmaximal, complemented
6#20246263C212yesmaximal, complemented
7C22⋊C4×Dic94C212yesmaximal, complemented
8#20246116C214yesmaximal, complemented
9#20246002C211yesmaximal, characteristic
10#20246000C211yesmaximal, characteristic
11C4×#13094001C214yesmaximal, complemented
12C2×#15688981C211yesmaximal, characteristic
13#20245741C211yesmaximal, characteristic
14C2×C22⋊C4×Dic47C211yesmaximal, characteristic
15C47×#2273C211yesmaximal, characteristic
16C23×Dic94C2211yescharacteristic
17C24×Dic47C2211yescharacteristic
18C2×#13094001C4116yescomplemented
19C2×#13094001C2212yes—
20C2×#13094001C2212yes—
21C2×#13094001C2212yes—
22C2×#13094001C2212yes—
23C2×C4×Dic94C2214yescomplemented
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2212yes—
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C4×Dic47C2212yes—
32#15689029C2214yescomplemented
33#15689027C2214yescomplemented
34#15689027C2214yescomplemented
35#15689021C2214yescomplemented
36#15689020C2214yescomplemented
37#15689020C2214yescomplemented
38#15689010C2214yescomplemented
39#15689010C2214yescomplemented
40#15689007C2214yescomplemented
41#15689007C2214yescomplemented
42#15689006C2214yescomplemented
43#15689006C2214yescomplemented
44#15688998C2214yes—
45#15688998C2214yes—
46#15688996C2214yes—
47#15688995C2214yes—
48#15688983C2212yes—
49#15688983C2212yes—
50#15688981C2212yes—
51#15688981C2212yes—
52#15688981C2212yes—
53#15688981C2212yes—
54#15688981C2212yes—
55#15688981C2212yes—
56C4×Dic47⋊C4C2214yescomplemented
57C4×Dic47⋊C4C2214yescomplemented
58C4×C4⋊Dic47C2214yescomplemented
59C22⋊C4×Dic47C2212yes—
60C22⋊C4×Dic47C2214yes—
61C22⋊C4×Dic47C2212yes—
62C22⋊C4×Dic47C2212yes—
63C22⋊C4×Dic47C2212yes—
64C22⋊C4×Dic47C2212yes—
65C22⋊C4×Dic47C2212yes—
66C4×C22⋊Dic47C2214yes—
67C2×C47⋊#95C2212yes—
68C2×C47⋊#95C2212yes—
69C22×C22⋊C4×C47C2211yescharacteristic
70C22×C22⋊C4×C47C2211yescharacteristic
71C22×C22⋊C4×C47C2211yescharacteristic
72C4×C22⋊C4×C47C2214yes—
73C4×C22⋊C4×C47C2214yes—
74C4×C22⋊C4×C47C2212yes—
75C4×C22⋊C4×C47C2212yes—
76C22×Dic94—44no—
77C22×Dic94C2×C418yescomplemented
78C22×Dic94C2312yes—
79C22×Dic94C2312yes—
80C23×Dic47—44no—
81C23×Dic47C2×C418yes—
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2312yes—
86C23×Dic47C2312yes—
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C23×Dic47C2311yescharacteristic
92#13094001C2×C4116yescomplemented
93#13094001C2×C4116yescomplemented
94#13094001C2×C4116yescomplemented
95#13094001C2×C4116yescomplemented
96C4×Dic94—48no—
97C2×C4⋊Dic47C2×C418yescomplemented
98C2×C4⋊Dic47C2314yes—
99C2×C4⋊Dic47C2314yes—
100C2×C4⋊Dic47C2312yes—
101C2×C4⋊Dic47C2312yes—
102C2×Dic47⋊C4—44no—
103C2×Dic47⋊C4C2×C418yescomplemented
104C2×Dic47⋊C4C2×C418yescomplemented
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2312yes—
110C2×Dic47⋊C4C2312yes—
111C2×Dic47⋊C4C2312yes—
112C2×Dic47⋊C4C2312yes—
113C2×C22⋊Dic47—24no—
114C2×C22⋊Dic47—24no—
115C2×C22⋊Dic47C2×C418yes—
116C2×C22⋊Dic47C2312yes—
117C2×C22⋊Dic47C2312yes—
118C2×C22⋊Dic47C2312yes—
119C2×C22⋊Dic47C2312yes—
120C2×C22⋊Dic47C2312yes—
121C2×C22⋊Dic47C2312yes—
122C2×C4×Dic47—44no—
123C2×C4×Dic47C2314yes—
124C2×C4×Dic47C2314yes—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C25×C47C2311yescharacteristic
138C23×C4×C47C2312yes—
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2312yes—
142C2×C22⋊C4×C47—24no—
143C2×C22⋊C4×C47C2×C418yes—
144C2×C22⋊C4×C47Q818yescomplemented
145C2×C22⋊C4×C47C2312yes—
146C2×C22⋊C4×C47C2312yes—
147C2×C22⋊C4×C47C2312yes—
148C2×C22⋊C4×C47C2312yes—
149C2×C22⋊C4×C47C2312yes—
150C2×C22⋊C4×C47C2312yes—
151C2×C42×C47C2314yes—
152C2×C42×C47C2314yes—
153#95×C47C2314yes—
154#95×C47C2314yes—
155C24×C47—42no—
156C24×C47—42no—
157C24×C47C22×C414yes—
158C24×C47C2×Q814yes—
159C24×C47#4114yes—
160C24×C47C2411yescharacteristic
161C24×C47C2411yescharacteristic
162C24×C47C2411yescharacteristic
163C22×C4×C47—24no—
164C22×C4×C47—42no—
165C22×C4×C47—42no—
166C22×C4×C47—42no—
167C22×C4×C47—42no—
168C22×C4×C47—42no—
169C22×C4×C47—42no—
170C22×C4×C47C22×C414yes—
171C22×C4×C47C22×C414yes—
172C22×C4×C47C2×Q818yescomplemented
173C22×C4×C47C2414yes—
174C22×C4×C47C2412yes—
175C22×C4×C47C2412yes—
176C22×C4×C47C2414yes—
177C22×Dic47—24no—
178C22×Dic47—24no—
179C22×Dic47—24no—
180C22×Dic47—24no—
181C22×Dic47—24no—
182C22×Dic47—416no—
183C22×Dic47—42no—
184C22×Dic47—42no—
185C22×Dic47—42no—
186C22×Dic47—42no—
187C22×Dic47—42no—
188C22×Dic47—42no—
189C22×Dic47—42no—
190C22×Dic47—42no—
191C22×Dic47—42no—
192C22×Dic47C22×C414yes—
193C22×Dic47C22×C414yes—
194C22×Dic47C22×C414yes—
195C22×Dic47C22×C414yes—
196C22×Dic47C22×C414yes—
197C22×Dic47C22×C414yes—
198C22×Dic47C22×C414yes—
199C22×Dic47C22×C414yes—
200C22×Dic47C2414yes—
201C22×Dic47C2414yes—
202C22×Dic47C2411yescharacteristic
203C22×Dic47C2411yescharacteristic
204C22×Dic47C2412yes—
205C22×Dic47C2412yes—
206C22×Dic47C2411yescharacteristic
207C22×Dic47C2411yescharacteristic
208C2×Dic94—28no—
209C2×Dic94—416no—
210C2×Dic94—44no—
211C2×Dic94C22×C418yes—
212C2×Dic94C22×C418yes—
213C22⋊C4×C47—24no—
214C22⋊C4×C47—24no—
215C22⋊C4×C47C22×C418yes—
216C22⋊C4×C47C22×C418yes—
217C22⋊C4×C47C2×Q818yes—
218C22⋊C4×C47C2×Q818yescomplemented
219C42×C47—44no—
220C42×C47—44no—
221C22⋊Dic47—24no—
222C22⋊Dic47—24no—
223C22⋊Dic47—24no—
224C22⋊Dic47—24no—
225C22⋊Dic47C22×C418yes—
226C22⋊Dic47C22×C418yes—
227C4⋊Dic47—44no—
228C4⋊Dic47—44no—
229C4⋊Dic47C22×C418yes—
230C4⋊Dic47C22×C418yes—
231Dic47⋊C4—28no—
232Dic47⋊C4—44no—
233Dic47⋊C4—44no—
234Dic47⋊C4—44no—
235Dic47⋊C4C22×C418yes—
236Dic47⋊C4C22×C418yes—
237Dic47⋊C4C22×C418yes—
238Dic47⋊C4C22×C418yes—
239C4×Dic47—28no—
240C4×Dic47—44no—
241C4×Dic47—44no—
242C4×Dic47—44no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—22no—
248C23×C47—22no—
249C23×C47—44no—
250C23×C47—44no—
251C23×C47—48no—
252C23×C47—48no—
253C23×C47C4×Q8116yescomplemented
254C23×C47C23×C412yes—
255C23×C47C23×C412yes—
256C23×C47C23×C412yes—
257C23×C47C22×Q812yes—
258C23×C47C22×Q812yes—
259C23×C47C22×Q812yes—
260C23×C47C2×#4112yes—
261C23×C47C2×#4112yes—
262C23×C47C2×#4112yes—
263C23×C47C2511yescharacteristic
264C2×C4×C47—24no—
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—44no—
272C2×C4×C47—44no—
273C2×C4×C47—48no—
274C2×C4×C47—84no—
275C2×C4×C47C23×C414yes—
276C2×C4×C47C23×C414yes—
277C2×C4×C47C22×Q818yes—
278C2×Dic47—22no—
279C2×Dic47—24no—
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—24no—
283C2×Dic47—28no—
284C2×Dic47—28no—
285C2×Dic47—28no—
286C2×Dic47—24no—
287C2×Dic47—24no—
288C2×Dic47—24no—
289C2×Dic47—24no—
290C2×Dic47—24no—
291C2×Dic47—24no—
292C2×Dic47—44no—
293C2×Dic47—44no—
294C2×Dic47—44no—
295C2×Dic47—44no—
296C2×Dic47—44no—
297C2×Dic47—48no—
298C2×Dic47—84no—
299C2×Dic47C23×C414yes—
300C2×Dic47C23×C412yes—
301C2×Dic47C23×C412yes—
302C2×Dic47C23×C412yes—
303C2×Dic47C23×C414yes—
304C2×Dic47C23×C412yes—
305C2×Dic47H(5,𝔽2)14yes—
306Dic94—216no—
307Dic94—48no—
308#34212—471nomaximal, Sylow
309C22×C47—22no—
310C22×C47—22no—
311C22×C47—22no—
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—24no—
316C22×C47—24no—
317C22×C47—24no—
318C22×C47—24no—
319C22×C47—24no—
320C22×C47—24no—
321C22×C47—416no—
322C22×C47C2×C4×Q814yes—
323C22×C47C2×C4×Q814yes—
324C22×C47C2×C4×Q814yes—
325C22×C47C24×C411yescharacteristic
326C22×C47C23×Q811yescharacteristic
327C22×C47C22×#4111yescharacteristic
328C22×C47C2×H(5,𝔽2)12yes—
329C22×C47#58512yes—
330C4×C47—24no—
331C4×C47—24no—
332C4×C47—28no—
333C4×C47—44no—
334Dic47—24no—
335Dic47—22no—
336Dic47—22no—
337Dic47—22no—
338Dic47—24no—
339Dic47—44no—
340Dic47—44no—
341Dic47#51814yes—
342C22×C22⋊Q8—471no—
343#2368—474no—
344#2360—474no—
345#2345—472no—
346#2345—472no—
347#2345—472no—
348Q8×C22⋊C4—472no—
349#2329—474no—
350#2315—471no—
351#2315—471no—
352C4×C22⋊Q8—474no—
353C2×#380—471no—
354#2273—471no—
355#2273D4711yescharacteristic
356C2×C4×C22⋊C4—471no—
357C2×C47—24no—
358C2×C47—24no—
359C2×C47—24no—
360C2×C47C22×C4×Q811yescharacteristic
361C2×C47C2×#51811yescharacteristic
362C2×C47#342811yescharacteristic
363C2×C47#350112yes—
364C2×C47#350512yes—
365C23×Q8—471no—
366C24×C4—471no—
367C2×C22⋊Q8—4716no—
368C2×C22⋊Q8—472no—
369C2×C22⋊Q8—472no—
370C2×C22⋊Q8—472no—
371C2×C22⋊Q8—472no—
372C2×C4×Q8—474no—
373C22×C4⋊C4—471no—
374C22×C4⋊C4—471no—
375C22×C4⋊C4—471no—
376C22×C4⋊C4—472no—
377C22×C22⋊C4—471no—
378C22×C22⋊C4—471no—
379C22×C22⋊C4—471no—
380C22×C22⋊C4C2×D4711yescharacteristic
381C22×C22⋊C4C2×D4711yescharacteristic
382C22×C22⋊C4C2×D4711yescharacteristic
383C22×C42—472no—
384#391—474no—
385#391—474no—
386#391—474no—
387#389—474no—
388#389—474no—
389#389—474no—
390#387—474no—
391#387—474no—
392#387—474no—
393#387—474no—
394#387—474no—
395#387—474no—
396#385—474no—
397#385—474no—
398#385—474no—
399#385—474no—
400#380—472no—
401#380—472no—
402#380—472no—
403#380—472no—
404#380—472no—
405#380—472no—
406#380—472no—
407#380—472no—
408C4×C4⋊C4—474no—
409C4×C4⋊C4—474no—
410C4×C4⋊C4—474no—
411C4×C22⋊C4—474no—
412C4×C22⋊C4—472no—
413C4×C22⋊C4—472no—
414C4×C22⋊C4—472no—
415C4×C22⋊C4—472no—
416C4×C22⋊C4—472no—
417C4×C22⋊C4—474no—
418C4×C22⋊C4—472no—
419C4×C22⋊C4C2×D4714yes—
420C4×C22⋊C4C2×D4712yes—
421C4×C22⋊C4C2×D4712yes—
422C4×C22⋊C4C2×D4714yes—
423C2×#95—472no—
424C2×#95—472no—
425C47#3421211yescharacteristic, complemented, Sylow
426C25C22×D4711yescharacteristic
427C22×Q8—478no—
428C22×Q8—472no—
429C22×Q8—472no—
430C22×Q8—1884no—
431C23×C4—471no—
432C23×C4—471no—
433C23×C4—471no—
434C23×C4—478no—
435C23×C4—471no—
436C23×C4—471no—
437C23×C4—471no—
438C23×C4—471no—
439C23×C4—471no—
440C23×C4—472no—
441C23×C4—472no—
442C23×C4—1884no—
443C23×C4C22×D4712yes—
444C23×C4C22×D4712yes—
445C23×C4C22×D4711yescharacteristic
446C23×C4C22×D4711yescharacteristic
447C22⋊Q8—4716no—
448C22⋊Q8—4716no—
449C22⋊Q8—4716no—
450C22⋊Q8—4716no—
451C4×Q8—1888no—
452C2×C4⋊C4—478no—
453C2×C4⋊C4—478no—
454C2×C4⋊C4—478no—
455C2×C4⋊C4—472no—
456C2×C4⋊C4—472no—
457C2×C4⋊C4—472no—
458C2×C4⋊C4—472no—
459C2×C4⋊C4—472no—
460C2×C4⋊C4—472no—
461C2×C4⋊C4—474no—
462C2×C4⋊C4—474no—
463C2×C4⋊C4—474no—
464C2×C4⋊C4—474no—
465C2×C4⋊C4—474no—
466C2×C4⋊C4—474no—
467C2×C4⋊C4—1884no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—478no—
470C2×C22⋊C4—472no—
471C2×C22⋊C4—472no—
472C2×C22⋊C4—472no—
473C2×C22⋊C4—472no—
474C2×C22⋊C4—472no—
475C2×C22⋊C4—472no—
476C2×C22⋊C4—944no—
477C2×C22⋊C4—944no—
478C2×C22⋊C4Dic9418yescomplemented
479C2×C22⋊C4C4×D4718yes—
480C2×C22⋊C4C22×D4712yes—
481C2×C22⋊C4C22×D4712yes—
482C2×C22⋊C4C22×D4712yes—
483C2×C22⋊C4C22×D4712yes—
484C2×C22⋊C4C22×D4712yes—
485C2×C22⋊C4C22×D4712yes—
486C2×C42—474no—
487C2×C42—474no—
488C2×C42—474no—
489C2×C42—474no—
490C2×C42—1884no—
491C2×C42C22×D4714yes—
492C2×C42C22×D4714yes—
493#95—474no—
494#95—474no—
495#95—474no—
496#95—474no—
497#95—474no—
498#95—474no—
499#95—474no—
500#95—474no—
501#95—474no—
502#95—474no—
503#95C22×D4714yes—
504#95C22×D4714yes—
505C24—42no—
506C24—42no—
507C24C2×Dic9414yes—
508C24C2×C4×D4714yes—
509C24#1062535014yes—
510C24C23×D4711yescharacteristic
511C24C23×D4711yescharacteristic
512C24C23×D4711yescharacteristic
513C2×Q8—478no—
514C2×Q8—478no—
515C2×Q8—948no—
516C2×Q8—1884no—
517C2×Q8—18816no—
518C22×C4—24no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—471no—
526C22×C4—474no—
527C22×C4—474no—
528C22×C4—474no—
529C22×C4—471no—
530C22×C4—471no—
531C22×C4—472no—
532C22×C4—472no—
533C22×C4—471no—
534C22×C4—474no—
535C22×C4—474no—
536C22×C4—474no—
537C22×C4—474no—
538C22×C4—474no—
539C22×C4—474no—
540C22×C4—474no—
541C22×C4—944no—
542C22×C4—944no—
543C22×C4—944no—
544C22×C4—944no—
545C22×C4—944no—
546C22×C4—18816no—
547C22×C4—1882no—
548C22×C4—1882no—
549C22×C4—1882no—
550C22×C4—1882no—
551C22×C4—1882no—
552C22×C4—1882no—
553C22×C4—1882no—
554C22×C4—1882no—
555C22×C4—1882no—
556C22×C4C2×Dic9418yescomplemented
557C22×C4C2×C4×D4714yes—
558C22×C4C2×C4×D4714yes—
559C22×C4C23×D4714yes—
560C22×C4C23×D4712yes—
561C22×C4C23×D4712yes—
562C22×C4C23×D4714yes—
563C4⋊C4—478no—
564C4⋊C4—478no—
565C4⋊C4—478no—
566C4⋊C4—478no—
567C4⋊C4—478no—
568C4⋊C4—478no—
569C4⋊C4—948no—
570C4⋊C4—1884no—
571C4⋊C4—1884no—
572C4⋊C4—1884no—
573C4⋊C4—1884no—
574C4⋊C4—1884no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—478no—
578C22⋊C4—478no—
579C22⋊C4—944no—
580C22⋊C4—944no—
581C22⋊C4—944no—
582C22⋊C4—944no—
583C22⋊C4C2×Dic9418yes—
584C22⋊C4C2×Dic9418yescomplemented
585C22⋊C4C2×C4×D4718yes—
586C22⋊C4C2×C4×D4718yes—
587C42—44no—
588C42—44no—
589C42—948no—
590C42—1884no—
591C42—1884no—
592C42—1884no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—44no—
600C23—48no—
601C23—44no—
602C23—48no—
603C23C4×Dic94116yescomplemented
604C23C22×C4×D4712yes—
605C23C22×C4×D4712yes—
606C23C22×C4×D4712yes—
607C23C22×Dic9412yes—
608C23C22×Dic9412yes—
609C23C22×Dic9412yes—
610C23C2×#1062535012yes—
611C23C2×#1062535012yes—
612C23C2×#1062535012yes—
613C23C24×D4711yescharacteristic
614Q8—9416no—
615Q8—1888no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—48no—
624C2×C4—44no—
625C2×C4—44no—
626C2×C4—84no—
627C2×C4—472no—
628C2×C4—474no—
629C2×C4—474no—
630C2×C4—474no—
631C2×C4—472no—
632C2×C4—472no—
633C2×C4—472no—
634C2×C4—948no—
635C2×C4—948no—
636C2×C4—948no—
637C2×C4—942no—
638C2×C4—944no—
639C2×C4—942no—
640C2×C4—942no—
641C2×C4—944no—
642C2×C4—944no—
643C2×C4—944no—
644C2×C4—944no—
645C2×C4—944no—
646C2×C4—944no—
647C2×C4—944no—
648C2×C4—3764no—
649C2×C4—1884no—
650C2×C4—1884no—
651C2×C4—1884no—
652C2×C4—1884no—
653C2×C4—1884no—
654C2×C4—1888no—
655C2×C4C22×C4×D4714yes—
656C2×C4C22×C4×D4714yes—
657C2×C4C22×Dic9418yes—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—24no—
665C22—24no—
666C22—24no—
667C22—24no—
668C22—24no—
669C22—24no—
670C22—416no—
671C22C2×C4×Dic9414yes—
672C22C2×C4×Dic9414yes—
673C22C2×C4×Dic9414yes—
674C22C23×C4×D4711yescharacteristic
675C22C23×Dic9411yescharacteristic
676C22C22×#1062535011yescharacteristic
677C22H(5,𝔽2)×D4712yes—
678C22#1568995812yes—
679C4—24no—
680C4—24no—
681C4—28no—
682C4—44no—
683C4—474no—
684C4—942no—
685C4—942no—
686C4—942no—
687C4—944no—
688C4—944no—
689C4—1884no—
690C4—1884no—
691C2—24no—
692C2—24no—
693C2—24no—
694C2C22×C4×Dic9411yescharacteristic
695C2#518×D4711yescharacteristic
696C2#2025658611yescharacteristic
697C2#2025718612yes—
698C2#2025721812yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2273C2
socle, cosocleC23×C47C25
prime radicalC25×C47C23
hypercenter#2273D47
hypocenterC47#34212
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2273

Complements

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

NH ≅ G/Ntype
2. #20246466C2semidirect
3. #20246394C2semidirect
4. #20246266C2semidirect
5. #20246266C2semidirect
6. #20246263C2semidirect
7. C22⋊C4×Dic94C2semidirect
8. #20246116C2semidirect
11. C4×#13094001C2semidirect
18. C2×#13094001C4semidirect
23. C2×C4×Dic94C22semidirect
32. #15689029C22semidirect
33. #15689027C22semidirect
34. #15689027C22semidirect
35. #15689021C22semidirect
36. #15689020C22semidirect
37. #15689020C22semidirect
38. #15689010C22semidirect
39. #15689010C22semidirect
40. #15689007C22semidirect
41. #15689007C22semidirect
42. #15689006C22semidirect
43. #15689006C22semidirect
56. C4×Dic47⋊C4C22semidirect
57. C4×Dic47⋊C4C22semidirect
58. C4×C4⋊Dic47C22semidirect
77. C22×Dic94C2×C4semidirect
92. #13094001C2×C4semidirect
93. #13094001C2×C4semidirect
94. #13094001C2×C4semidirect
95. #13094001C2×C4semidirect
97. C2×C4⋊Dic47C2×C4semidirect
103. C2×Dic47⋊C4C2×C4semidirect
104. C2×Dic47⋊C4C2×C4semidirect
144. C2×C22⋊C4×C47Q8semidirect
172. C22×C4×C47C2×Q8semidirect
218. C22⋊C4×C47C2×Q8semidirect
253. C23×C47C4×Q8semidirect
425. C47#34212semidirect
478. C2×C22⋊C4Dic94semidirect
556. C22×C4C2×Dic94semidirect
584. C22⋊C4C2×Dic94semidirect
603. C23C4×Dic94semidirect

Maximal subgroups

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

subgroupindex
C22×#130940012
#202464662
#202463942
#202462662
#202462632
C22⋊C4×Dic942
#202461162
#202460022
#202460002
C4×#130940012
C2×#156889812
#202457412
C2×C22⋊C4×Dic472
C47×#22732
#3421247