Finite Group Databasebeta

← C2×#20247066 #26384928

Subgroups — C2×#20247066 #26384928

Order 12032.

3006 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×#13094001C211yesmaximal, characteristic
2C22×#13093983C211yesmaximal, characteristic
3#20247066C2116yesmaximal, direct product factor
4C2×#15689065C211yesmaximal, characteristic, complemented
5C2×#15689057C211yesmaximal, characteristic, complemented
6C2×#15689055C211yesmaximal, characteristic, complemented
7C2×#15689044C211yesmaximal, characteristic, complemented
8C2×#15689027C211yesmaximal, characteristic, complemented
9C2×#15689020C211yesmaximal, characteristic, complemented
10C2×#15689010C211yesmaximal, characteristic, complemented
11C2×#15689006C211yesmaximal, characteristic, complemented
12C2×#15688998C211yesmaximal, characteristic
13C2×#15688995C211yesmaximal, characteristic
14C2×#15688981C211yesmaximal, characteristic
15C22×C47⋊#95C211yesmaximal, characteristic
16C2×C47×#381C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C2×#13094001—28no—
21C2×#13094001C2218yes—
22C2×#13093983—28no—
23C2×#13093983C2218yes—
24C22×C4⋊Dic47C2211yescharacteristic
25C22×C4⋊Dic47C2211yescharacteristic
26C22×C4⋊Dic47C2211yescharacteristic
27C22×C4⋊Dic47C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×C22⋊Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39#15689065C2218yescomplemented
40#15689057C2218yescomplemented
41#15689055C2218yescomplemented
42#15689044C2218yescomplemented
43#15689027C2218yescomplemented
44#15689020C2218yescomplemented
45#15689010C2218yescomplemented
46#15689006C2218yescomplemented
47#15688998C2218yes—
48#15688995C2218yes—
49#15688981C2218yes—
50C2×C47⋊#95C2218yes—
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C24×C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C47×#381C2218yes—
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C22×Dic94—24no—
70C22×Dic94—24no—
71C22×Dic94—42no—
72C22×Dic94C2314yes—
73C23×Dic47—24no—
74C23×Dic47—24no—
75C23×Dic47—24no—
76C23×Dic47—24no—
77C23×Dic47—42no—
78C23×Dic47—42no—
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2314yes—
84C23×Dic47C2314yes—
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89#13094001—232no—
90#13093983—232no—
91C2×C4⋊Dic47—24no—
92C2×C4⋊Dic47—24no—
93C2×C4⋊Dic47—24no—
94C2×C4⋊Dic47—24no—
95C2×C4⋊Dic47—42no—
96C2×C4⋊Dic47C2314yes—
97C2×C4⋊Dic47C2314yes—
98C2×C4⋊Dic47C2314yes—
99C2×C4⋊Dic47C2314yes—
100C2×C4⋊Dic47C2314yes—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—24no—
105C2×Dic47⋊C4—42no—
106C2×Dic47⋊C4—42no—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×C22⋊Dic47—24no—
114C2×C22⋊Dic47D418yes—
115C2×C22⋊Dic47C2314yes—
116C2×C22⋊Dic47C2314yes—
117C2×C4×Dic47—24no—
118C2×C4×Dic47—24no—
119C2×C4×Dic47C2314yes—
120C2×C4×Dic47C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C25×C47C2311yescharacteristic
132C23×C4×C47—24no—
133C23×C4×C47—24no—
134C23×C4×C47Q818yescomplemented
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2314yes—
142C2×C22⋊C4×C47—24no—
143C2×C22⋊C4×C47—24no—
144C2×C22⋊C4×C47C2314yes—
145C2×C22⋊C4×C47C2314yes—
146#95×C47C2314yes—
147#95×C47C2314yes—
148#95×C47C2314yes—
149#95×C47C2314yes—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47C2×D414yes—
155C24×C47C2×Q814yes—
156C24×C47#4114yes—
157C24×C47C2412yes—
158C24×C47C2411yescharacteristic
159C22×C4×C47—232no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—28no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—28no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47C2×Q814yes—
179C22×C4×C47C2×Q814yes—
180C22×C4×C47C2×Q8116yescomplemented
181C22×C4×C47C2412yes—
182C22×C4×C47C2412yes—
183C22×C4×C47C2412yes—
184C22×C4×C47C2412yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—28no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—28no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—28no—
210C22×Dic47—28no—
211C22×Dic47—44no—
212C22×Dic47—44no—
213C22×Dic47—416no—
214C22×Dic47—416no—
215C22×Dic47C2×D414yes—
216C22×Dic47C2×D414yes—
217C22×Dic47#4114yes—
218C22×Dic47#4114yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C2×Dic94—28no—
228C2×Dic94—28no—
229C2×Dic94—44no—
230C2×Dic94—416no—
231C22⋊C4×C47—28no—
232C22⋊C4×C47—28no—
233C22⋊Dic47—28no—
234C22⋊Dic47C2×D4116yes—
235C4⋊Dic47—28no—
236C4⋊Dic47—28no—
237C4⋊Dic47—28no—
238C4⋊Dic47—28no—
239C4⋊Dic47—44no—
240Dic47⋊C4—28no—
241Dic47⋊C4—28no—
242Dic47⋊C4—28no—
243Dic47⋊C4—28no—
244Dic47⋊C4—44no—
245Dic47⋊C4—44no—
246C4×Dic47—28no—
247C4×Dic47—28no—
248C23×C47—28no—
249C23×C47—28no—
250C23×C47—28no—
251C23×C47—28no—
252C23×C47—28no—
253C23×C47—28no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47C22⋊Q8116yes—
259C23×C47C22×D414yes—
260C23×C47C22×D412yes—
261C23×C47C22×Q814yes—
262C23×C47C22×Q812yes—
263C23×C47C2×#4112yes—
264C23×C47C2×#4112yes—
265C23×C47C2×#4114yes—
266C23×C47C2×#4112yes—
267C23×C47H(5,𝔽2)12yes—
268C23×C472−1+412yes—
269C23×C47C2511yescharacteristic
270C2×C4×C47—28no—
271C2×C4×C47—28no—
272C2×C4×C47—232no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—44no—
290C2×C4×C47—44no—
291C2×C4×C47—44no—
292C2×C4×C47—44no—
293C2×C4×C47C22×Q814yes—
294C2×C4×C47C22×Q814yes—
295C2×Dic47—28no—
296C2×Dic47—28no—
297C2×Dic47—28no—
298C2×Dic47—28no—
299C2×Dic47—22no—
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—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—416no—
320C2×Dic47—416no—
321C2×Dic47—44no—
322C2×Dic47—44no—
323C2×Dic47—44no—
324C2×Dic47—44no—
325C2×Dic47C22×D414yes—
326C2×Dic47C22×D414yes—
327C2×Dic47C2×#4114yes—
328C2×Dic47C2×#4114yes—
329Dic94—416no—
330C2×#2438—471nomaximal, Sylow
331C22×C47—24no—
332C22×C47—24no—
333C22×C47—232no—
334C22×C47—24no—
335C22×C47—24no—
336C22×C47—24no—
337C22×C47—24no—
338C22×C47C2×C22⋊Q818yes—
339C22×C47C2×C22⋊Q814yes—
340C22×C47#53314yes—
341C22×C47#54414yes—
342C22×C47#54614yes—
343C22×C47#54714yes—
344C22×C47#55114yes—
345C22×C47#55214yes—
346C22×C47C23×D411yescharacteristic
347C22×C47C23×Q811yescharacteristic
348C22×C47C22×#4111yescharacteristic
349C22×C47C22×#4111yescharacteristic
350C22×C47C22×#4111yescharacteristic
351C22×C47C2×H(5,𝔽2)11yescharacteristic
352C22×C47C2×2−1+411yescharacteristic
353C4×C47—24no—
354C4×C47—24no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47—42no—
358C4×C47—42no—
359Dic47—24no—
360Dic47—24no—
361Dic47—24no—
362Dic47—24no—
363Dic47—42no—
364Dic47—42no—
365Dic47—42no—
366Dic47—42no—
367C22×C22⋊Q8—471no—
368C22×#117—471no—
369#2438—4716no—
370C2×#400—471no—
371C2×#398—471no—
372C2×#398—471no—
373C2×#395—471no—
374C2×#391—471no—
375C2×#389—471no—
376C2×#387—471no—
377C2×#387—471no—
378C2×#385—471no—
379C2×#385—471no—
380C2×#381D4711yescharacteristic
381C2×#380—471no—
382C22×#95—471no—
383C2×C47—28no—
384C2×C47#243818yescomplemented
385C2×C47C22×C22⋊Q811yescharacteristic
386C2×C47C2×#53311yescharacteristic
387C2×C47C2×#54411yescharacteristic
388C2×C47C2×#54611yescharacteristic
389C2×C47C2×#54711yescharacteristic
390C2×C47C2×#55111yescharacteristic
391C2×C47C2×#55211yescharacteristic
392C23×Q8—471no—
393C24×C4—471no—
394C24×C4—471no—
395C24×C4C2×D4711yescharacteristic
396C2×C22⋊Q8—478no—
397C2×C22⋊Q8—948no—
398C2×#117—478no—
399C2×#117—948no—
400C22×C4⋊C4—471no—
401C22×C4⋊C4—471no—
402C22×C4⋊C4—471no—
403C22×C4⋊C4—471no—
404C22×C4⋊C4—471no—
405C22×C4⋊C4—471no—
406C22×C4⋊C4—471no—
407C22×C4⋊C4—471no—
408C22×C4⋊C4—471no—
409C22×C4⋊C4—471no—
410C22×C4⋊C4—471no—
411C22×C22⋊C4—471no—
412C22×C22⋊C4—471no—
413C22×C22⋊C4C2×D4711yescharacteristic
414C22×C22⋊C4C2×D4711yescharacteristic
415C22×C42—471no—
416C22×C42—471no—
417#400—478no—
418#398—478no—
419#398—478no—
420#395—478no—
421#391—478no—
422#389—478no—
423#387—478no—
424#387—478no—
425#385—478no—
426#385—478no—
427#381C2×D4718yes—
428#380—478no—
429C2×#95—471no—
430C2×#95—471no—
431C2×#95—471no—
432C2×#95—471no—
433C2×#95—471no—
434C2×#95—471no—
435C2×#95—471no—
436C2×#95—471no—
437C2×#95—478no—
438C2×#95—471no—
439C2×#95—471no—
440C2×#95C2×D4711yescharacteristic
441C2×#95C2×D4711yescharacteristic
442C2×#95C2×D4711yescharacteristic
443C2×#95C2×D4711yescharacteristic
444C47C2×#243811yescharacteristic, complemented, Sylow
445C25C22×D4711yescharacteristic
446C22×Q8—474no—
447C22×Q8—944no—
448C22×Q8—944no—
449C22×Q8—1882no—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—471no—
453C23×C4—471no—
454C23×C4—471no—
455C23×C4—471no—
456C23×C4—471no—
457C23×C4—471no—
458C23×C4—471no—
459C23×C4—471no—
460C23×C4—474no—
461C23×C4—474no—
462C23×C4—944no—
463C23×C4—944no—
464C23×C4—944no—
465C23×C4—944no—
466C23×C4—1882no—
467C23×C4—1882no—
468C23×C4Dic9418yescomplemented
469C23×C4C22×D4711yescharacteristic
470C23×C4C22×D4711yescharacteristic
471C23×C4C22×D4711yescharacteristic
472C23×C4C22×D4711yescharacteristic
473C23×C4C22×D4711yescharacteristic
474C23×C4C22×D4711yescharacteristic
475C23×C4C22×D4714yes—
476C22⋊Q8—9432no—
477#117—9432no—
478C2×C4⋊C4—474no—
479C2×C4⋊C4—474no—
480C2×C4⋊C4—474no—
481C2×C4⋊C4—474no—
482C2×C4⋊C4—474no—
483C2×C4⋊C4—474no—
484C2×C4⋊C4—474no—
485C2×C4⋊C4—474no—
486C2×C4⋊C4—474no—
487C2×C4⋊C4—474no—
488C2×C4⋊C4—474no—
489C2×C4⋊C4—944no—
490C2×C4⋊C4—944no—
491C2×C4⋊C4—944no—
492C2×C4⋊C4—944no—
493C2×C4⋊C4—944no—
494C2×C4⋊C4—944no—
495C2×C4⋊C4—944no—
496C2×C4⋊C4—944no—
497C2×C4⋊C4—1882no—
498C2×C4⋊C4—1882no—
499C2×C4⋊C4—1882no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—478no—
503C2×C22⋊C4—474no—
504C2×C22⋊C4—474no—
505C2×C22⋊C4—944no—
506C2×C22⋊C4C22×D4714yes—
507C2×C22⋊C4C22×D4714yes—
508C2×C42—474no—
509C2×C42—474no—
510C2×C42—944no—
511C2×C42—944no—
512#95—474no—
513#95—474no—
514#95—474no—
515#95—474no—
516#95—474no—
517#95—474no—
518#95—474no—
519#95—474no—
520#95—474no—
521#95—474no—
522#95C22×D4714yes—
523#95C22×D4714yes—
524#95C22×D4714yes—
525#95C22×D4714yes—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24C2×Dic9414yes—
531C24D4×D4714yes—
532C24#1062535214yes—
533C24C23×D4712yes—
534C24C23×D4711yescharacteristic
535C2×Q8—948no—
536C2×Q8—948no—
537C2×Q8—1884no—
538C2×Q8—18816no—
539C22×C4—232no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—28no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—28no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—474no—
559C22×C4—474no—
560C22×C4—474no—
561C22×C4—474no—
562C22×C4—472no—
563C22×C4—472no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—472no—
567C22×C4—472no—
568C22×C4—472no—
569C22×C4—472no—
570C22×C4—948no—
571C22×C4—948no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—948no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—948no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—942no—
594C22×C4—1884no—
595C22×C4—1884no—
596C22×C4—18816no—
597C22×C4—18816no—
598C22×C4C2×Dic9414yes—
599C22×C4C2×Dic9414yes—
600C22×C4C2×Dic94116yescomplemented
601C22×C4C23×D4712yes—
602C22×C4C23×D4712yes—
603C22×C4C23×D4712yes—
604C22×C4C23×D4712yes—
605C22×C4C23×D4712yes—
606C22×C4C23×D4712yes—
607C4⋊C4—948no—
608C4⋊C4—948no—
609C4⋊C4—948no—
610C4⋊C4—948no—
611C4⋊C4—948no—
612C4⋊C4—948no—
613C4⋊C4—948no—
614C4⋊C4—948no—
615C4⋊C4—1884no—
616C4⋊C4—1884no—
617C4⋊C4—1884no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—4716no—
621C22⋊C4—948no—
622C42—948no—
623C42—948no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23#13094001116yes—
635C23C2×D4×D4714yes—
636C23C2×D4×D4712yes—
637C23C22×Dic9414yes—
638C23C22×Dic9412yes—
639C23#41×D4712yes—
640C23#41×D4712yes—
641C23C2×#1062535214yes—
642C23C2×#1062535212yes—
643C23#1309407012yes—
644C23#1309407112yes—
645C23C24×D4711yescharacteristic
646Q8—18816no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—232no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—474no—
671C2×C4—474no—
672C2×C4—474no—
673C2×C4—474no—
674C2×C4—948no—
675C2×C4—948no—
676C2×C4—948no—
677C2×C4—948no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—18816no—
699C2×C4—18816no—
700C2×C4—1884no—
701C2×C4—1884no—
702C2×C4—1884no—
703C2×C4—1884no—
704C2×C4C22×Dic9414yes—
705C2×C4C22×Dic9414yes—
706C22—24no—
707C22—232no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—24no—
712C22—24no—
713C22C2×#1309400118yes—
714C22C2×#1309400114yes—
715C22#1568967614yes—
716C22#1568975114yes—
717C22#1568976514yes—
718C22#1568977114yes—
719C22#1568979614yes—
720C22#1568981014yes—
721C22C22×D4×D4711yescharacteristic
722C22C23×Dic9411yescharacteristic
723C22C2×#41×D4711yescharacteristic
724C22C2×#41×D4711yescharacteristic
725C22C22×#1062535211yescharacteristic
726C22C2×#1309407011yescharacteristic
727C22C2×#1309407111yescharacteristic
728C4—24no—
729C4—24no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—944no—
735C4—944no—
736C4—944no—
737C4—944no—
738C4—1882no—
739C4—1882no—
740C4—1882no—
741C4—1882no—
742C2—28no—
743C2#2024706618yesdirect product factor
744C2C22×#1309400111yescharacteristic
745C2C2×#1568967611yescharacteristic
746C2C2×#1568975111yescharacteristic
747C2C2×#1568976511yescharacteristic
748C2C2×#1568977111yescharacteristic
749C2C2×#1568979611yescharacteristic
750C2C2×#1568981011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#381C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#381D47
hypocenterC47C2×#2438
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #20247066C2direct (N × H)
4. C2×#15689065C2semidirect
5. C2×#15689057C2semidirect
6. C2×#15689055C2semidirect
7. C2×#15689044C2semidirect
8. C2×#15689027C2semidirect
9. C2×#15689020C2semidirect
10. C2×#15689010C2semidirect
11. C2×#15689006C2semidirect
39. #15689065C22semidirect
40. #15689057C22semidirect
41. #15689055C22semidirect
42. #15689044C22semidirect
43. #15689027C22semidirect
44. #15689020C22semidirect
45. #15689010C22semidirect
46. #15689006C22semidirect
134. C23×C4×C47Q8semidirect
180. C22×C4×C47C2×Q8semidirect
384. C2×C47#2438semidirect
444. C47C2×#2438semidirect
468. C23×C4Dic94semidirect
600. C22×C4C2×Dic94semidirect
743. C2#20247066direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940012
C22×#130939832
#202470662
C2×#156890652
C2×#156890572
C2×#156890552
C2×#156890442
C2×#156890272
C2×#156890202
C2×#156890102
C2×#156890062
C2×#156889982
C2×#156889952
C2×#156889812
C22×C47⋊#952
C2×C47×#3812
C2×#243847