Finite Group Databasebeta

← #26138261

Subgroups — #26138261

Order 12032.

2510 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic47⋊C4C211yesmaximal, characteristic
2C2×#15688998C211yesmaximal, characteristic
3C2×#15688996C211yesmaximal, characteristic
4C2×#15688995C211yesmaximal, characteristic
5C2×#15688992C212yesmaximal, complemented
6C2×#15688981C211yesmaximal, characteristic
7C2×C22⋊C4×Dic47C211yesmaximal, characteristic
8#20241652C212yesmaximal, complemented
9#20241651C212yesmaximal, complemented
10Dic47⋊#95C212yesmaximal, complemented
11C2×C47×#385C211yesmaximal, characteristic
12C24×Dic47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2212yes—
15C22×Dic47⋊C4—24no—
16C22×Dic47⋊C4—28no—
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2212yes—
21C22×Dic47⋊C4C2212yes—
22C22×Dic47⋊C4C2212yes—
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C4×Dic47C2212yes—
26#15688998—24no—
27#15688996—24no—
28#15688995—24no—
29#15688992—28no—
30#15688981—24no—
31C22⋊C4×Dic47C418yescomplemented
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2212yes—
38C24×C4×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2212yes—
40C22×C22⋊C4×C47C2211yescharacteristic
41C22×C22⋊C4×C47C2211yescharacteristic
42C47×#385—24no—
43C2×#95×C47C2212yes—
44C23×Dic47—24no—
45C23×Dic47—24no—
46C23×Dic47—22no—
47C23×Dic47—24no—
48C23×Dic47—22no—
49C23×Dic47—22no—
50C23×Dic47—42no—
51C23×Dic47C2×C414yes—
52C23×Dic47D414yes—
53C23×Dic47Q814yes—
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2312yes—
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2312yes—
59C23×Dic47C2311yescharacteristic
60C2×C4⋊Dic47—24no—
61C2×C4⋊Dic47—24no—
62C2×C4⋊Dic47—42no—
63C2×Dic47⋊C4—232no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4—24no—
69C2×Dic47⋊C4—24no—
70C2×Dic47⋊C4—22no—
71C2×Dic47⋊C4—22no—
72C2×Dic47⋊C4—24no—
73C2×Dic47⋊C4—24no—
74C2×Dic47⋊C4—24no—
75C2×Dic47⋊C4—24no—
76C2×Dic47⋊C4—24no—
77C2×Dic47⋊C4—42no—
78C2×Dic47⋊C4—42no—
79C2×Dic47⋊C4D418yes—
80C2×C22⋊Dic47—22no—
81C2×C22⋊Dic47—22no—
82C2×C22⋊Dic47—22no—
83C2×C22⋊Dic47C2×C414yes—
84C2×C22⋊Dic47D414yes—
85C2×C22⋊Dic47Q814yes—
86C2×C4×Dic47—24no—
87C2×C4×Dic47—24no—
88C2×C4×Dic47C2×C418yescomplemented
89C47⋊#95—24no—
90C47⋊#95—22no—
91C47⋊#95—22no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95C2×C418yescomplemented
95C25×C47C2311yescharacteristic
96C23×C4×C47—22no—
97C23×C4×C47—24no—
98C23×C4×C47—22no—
99C23×C4×C47—22no—
100C23×C4×C47—42no—
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2312yes—
104C23×C4×C47C2312yes—
105C2×C4⋊C4×C47—24no—
106C2×C4⋊C4×C47—24no—
107C2×C4⋊C4×C47—42no—
108C2×C22⋊C4×C47—22no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47C2×C414yes—
112C2×C22⋊C4×C47D414yes—
113C2×C22⋊C4×C47Q814yes—
114#95×C47—24no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47C22×C412yes—
120C24×C47C2×D412yes—
121C24×C47C2×D412yes—
122C24×C47C2×D412yes—
123C24×C47C2×Q812yes—
124C24×C47C2×Q812yes—
125C24×C47C2×Q812yes—
126C24×C47C2411yescharacteristic
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—28no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—48no—
149C22×C4×C47—48no—
150C22×C4×C47—44no—
151C22×C4×C47—44no—
152C22×C4×C47C22×C414yes—
153C22×C4×C47C2×D414yes—
154C22×C4×C47C2×D414yes—
155C22×C4×C47C2×Q814yes—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—216no—
163C22×Dic47—28no—
164C22×Dic47—216no—
165C22×Dic47—28no—
166C22×Dic47—28no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—48no—
184C22×Dic47—48no—
185C22×Dic47—44no—
186C22×Dic47—44no—
187C22×Dic47C4⋊C4116yescomplemented
188C22×Dic47C22×C412yes—
189C22×Dic47C22×C414yes—
190C22×Dic47C22×C412yes—
191C22×Dic47C2×D414yes—
192C22×Dic47C2×D412yes—
193C22×Dic47C2×D414yes—
194C22×Dic47C2×D412yes—
195C22×Dic47C2×D414yes—
196C22×Dic47C2×Q812yes—
197C22×Dic47C2×Q814yes—
198C22×Dic47C2×Q812yes—
199C22×Dic47#4114yes—
200C4⋊C4×C47—48no—
201C22⋊C4×C47—44no—
202C22⋊C4×C47C4⋊C4116yescomplemented
203C22⋊Dic47—44no—
204C22⋊Dic47C4⋊C4116yescomplemented
205C4⋊Dic47—48no—
206Dic47⋊C4—216no—
207Dic47⋊C4—216no—
208Dic47⋊C4—48no—
209Dic47⋊C4—48no—
210Dic47⋊C4—44no—
211Dic47⋊C4—44no—
212C4×Dic47—216no—
213C23×C47—24no—
214C23×C47—24no—
215C23×C47—22no—
216C23×C47—24no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—24no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—24no—
224C23×C47—24no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—24no—
228C23×C47—24no—
229C23×C47C2×C4⋊C414yes—
230C23×C47C2×C4⋊C414yes—
231C23×C47C2×C4⋊C414yes—
232C23×C47#12714yes—
233C23×C47C4⋊Q814yes—
234C23×C47C4⋊Q814yes—
235C23×C47C4⋊Q814yes—
236C23×C47C23×C411yescharacteristic
237C23×C47C22×D411yescharacteristic
238C23×C47C22×D411yescharacteristic
239C23×C47C22×D412yes—
240C23×C47C22×D411yescharacteristic
241C23×C47C22×Q811yescharacteristic
242C23×C47C22×Q811yescharacteristic
243C23×C47C22×Q811yescharacteristic
244C23×C47C2×#4112yes—
245C23×C47H(5,𝔽2)12yes—
246C23×C472−1+412yes—
247C2×C4×C47—24no—
248C2×C4×C47—24no—
249C2×C4×C47—24no—
250C2×C4×C47—24no—
251C2×C4×C47—24no—
252C2×C4×C47—24no—
253C2×C4×C47—24no—
254C2×C4×C47—24no—
255C2×C4×C47—24no—
256C2×C4×C47—416no—
257C2×C4×C47—42no—
258C2×C4×C47—42no—
259C2×C4×C47—42no—
260C2×C4×C47—42no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—42no—
268C2×C4×C47—42no—
269C2×C4×C47—42no—
270C2×C4×C47—42no—
271C2×C4×C47C2×C4⋊C418yescomplemented
272C2×Dic47—24no—
273C2×Dic47—24no—
274C2×Dic47—24no—
275C2×Dic47—22no—
276C2×Dic47—24no—
277C2×Dic47—22no—
278C2×Dic47—24no—
279C2×Dic47—24no—
280C2×Dic47—24no—
281C2×Dic47—24no—
282C2×Dic47—232no—
283C2×Dic47—24no—
284C2×Dic47—24no—
285C2×Dic47—24no—
286C2×Dic47—416no—
287C2×Dic47—42no—
288C2×Dic47—42no—
289C2×Dic47—42no—
290C2×Dic47—42no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301C2×Dic47C2×C4⋊C414yes—
302C2×Dic47C2×C4⋊C414yes—
303C2×Dic47C2×C4⋊C418yescomplemented
304C2×Dic47C4×D418yes—
305C2×Dic47#12014yes—
306C2×Dic47C22⋊Q818yes—
307C2×Dic47#12314yes—
308#13880—471nomaximal, Sylow
309C22×C47—24no—
310C22×C47—28no—
311C22×C47—28no—
312C22×C47—24no—
313C22×C47—24no—
314C22×C47—28no—
315C22×C47—28no—
316C22×C47—24no—
317C22×C47—24no—
318C22×C47—24no—
319C22×C47#38418yescomplemented
320C22×C47C22×C4⋊C411yescharacteristic
321C22×C47C22×C4⋊C411yescharacteristic
322C22×C47C22×C4⋊C411yescharacteristic
323C22×C47C2×C4×D412yes—
324C22×C47#52012yes—
325C22×C47C2×#12011yescharacteristic
326C22×C47C2×C22⋊Q812yes—
327C22×C47C2×#12311yescharacteristic
328C22×C47C2×#12711yescharacteristic
329C22×C47C2×C4⋊Q811yescharacteristic
330C22×C47C2×C4⋊Q811yescharacteristic
331C22×C47C2×C4⋊Q811yescharacteristic
332C22×C47#53511yescharacteristic
333C22×C47#53611yescharacteristic
334C22×C47#54412yes—
335C22×C47D4212yes—
336C22×C47D4212yes—
337C22×C47#54712yes—
338C22×C47#54712yes—
339C22×C47D4×Q812yes—
340C22×C47D4×Q812yes—
341C22×C47#55412yes—
342C22×C47#55412yes—
343C4×C47—28no—
344C4×C47—44no—
345C4×C47—81no—
346C4×C47—81no—
347Dic47—28no—
348Dic47—24no—
349Dic47—44no—
350Dic47—81no—
351Dic47—81no—
352Dic47#38518yescomplemented
353C23×C4⋊C4—471no—
354C2×#385—471no—
355C2×#385—471no—
356C2×#385—471no—
357C2×#385D4711yescharacteristic
358C2×#384—472no—
359C2×#380—471no—
360C2×C4×C22⋊C4—471no—
361#1444—472no—
362#1444—472no—
363C4⋊#95—472no—
364C2×C47—28no—
365C2×C47C2×#38411yescharacteristic
366C2×C47C2×#38511yescharacteristic
367C2×C47#231711yescharacteristic
368C2×C47D4×C4⋊C412yes—
369C2×C47D4×C4⋊C412yes—
370C2×C47#243311yescharacteristic
371C2×C47#243411yescharacteristic
372C2×C47#244012yes—
373C2×C47#244012yes—
374C2×C47#250111yescharacteristic
375C2×C47#250211yescharacteristic
376C24×C4—471no—
377C24×C4—471no—
378C24×C4C2×D4711yescharacteristic
379C22×C4⋊C4—472no—
380C22×C4⋊C4—472no—
381C22×C4⋊C4—471no—
382C22×C4⋊C4—471no—
383C22×C4⋊C4—472no—
384C22×C4⋊C4—472no—
385C22×C4⋊C4—472no—
386C22×C4⋊C4—948no—
387C22×C4⋊C4—944no—
388C22×C4⋊C4C2×D4712yes—
389C22×C22⋊C4—471no—
390C22×C22⋊C4—471no—
391C22×C22⋊C4C2×D4711yescharacteristic
392C22×C22⋊C4C2×D4711yescharacteristic
393C22×C42—472no—
394#385—24no—
395#385—944no—
396#385—944no—
397#385—944no—
398#384—948no—
399#380—944no—
400C4×C22⋊C4—478no—
401C2×#95—472no—
402C2×#95—472no—
403C2×#95—472no—
404C2×#95—472no—
405C2×#95—471no—
406C2×#95—471no—
407C2×#95C2×D4712yes—
408C47#1388011yescharacteristic, complemented, Sylow
409C25C22×D4711yescharacteristic
410C23×C4—22no—
411C23×C4—24no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—42no—
415C23×C4—471no—
416C23×C4—474no—
417C23×C4—474no—
418C23×C4—474no—
419C23×C4—472no—
420C23×C4—471no—
421C23×C4—472no—
422C23×C4—471no—
423C23×C4—471no—
424C23×C4—944no—
425C23×C4—944no—
426C23×C4—944no—
427C23×C4—942no—
428C23×C4—942no—
429C23×C4—942no—
430C23×C4—1882no—
431C23×C4C22×D4711yescharacteristic
432C23×C4C22×D4711yescharacteristic
433C23×C4C22×D4712yes—
434C23×C4C22×D4712yes—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—478no—
439C2×C4⋊C4—944no—
440C2×C4⋊C4—944no—
441C2×C4⋊C4—944no—
442C2×C4⋊C4—944no—
443C2×C4⋊C4—9432no—
444C2×C4⋊C4—944no—
445C2×C4⋊C4—944no—
446C2×C4⋊C4—942no—
447C2×C4⋊C4—942no—
448C2×C4⋊C4—944no—
449C2×C4⋊C4—944no—
450C2×C4⋊C4—944no—
451C2×C4⋊C4—944no—
452C2×C4⋊C4—944no—
453C2×C4⋊C4—944no—
454C2×C4⋊C4—944no—
455C2×C4⋊C4—1882no—
456C2×C4⋊C4—1882no—
457C2×C4⋊C4—1882no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—474no—
462C2×C22⋊C4—474no—
463C2×C22⋊C4—474no—
464C2×C22⋊C4—942no—
465C2×C22⋊C4—942no—
466C2×C22⋊C4—942no—
467C2×C22⋊C4Dic9414yes—
468C2×C22⋊C4C4×D4714yes—
469C2×C22⋊C4C22⋊D4714yes—
470C2×C42—478no—
471C2×C42—944no—
472C2×C42—944no—
473#95—24no—
474#95—478no—
475#95—942no—
476#95—942no—
477#95—944no—
478#95—944no—
479#95—944no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24C2×Dic9412yes—
485C24C2×C4×D4712yes—
486C24D4×D4712yes—
487C24D4×D4712yes—
488C24Q8×D4712yes—
489C24Q8×D4712yes—
490C24C2×C22⋊D4712yes—
491C24C23×D4711yescharacteristic
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—472no—
518C22×C4—474no—
519C22×C4—472no—
520C22×C4—472no—
521C22×C4—474no—
522C22×C4—4716no—
523C22×C4—472no—
524C22×C4—474no—
525C22×C4—474no—
526C22×C4—472no—
527C22×C4—474no—
528C22×C4—472no—
529C22×C4—474no—
530C22×C4—948no—
531C22×C4—9416no—
532C22×C4—9416no—
533C22×C4—948no—
534C22×C4—942no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—948no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—941no—
548C22×C4—941no—
549C22×C4—941no—
550C22×C4—941no—
551C22×C4—942no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—1888no—
558C22×C4—1888no—
559C22×C4—1884no—
560C22×C4—1884no—
561C22×C4C2×Dic9414yes—
562C22×C4C2×C4×D4714yes—
563C22×C4D4×D4714yes—
564C22×C4C2×C22⋊D4714yes—
565C4⋊C4—48no—
566C4⋊C4—9416no—
567C4⋊C4—9416no—
568C4⋊C4—1888no—
569C4⋊C4—1888no—
570C4⋊C4—1884no—
571C4⋊C4—1884no—
572C4⋊C4—1888no—
573C22⋊C4—44no—
574C22⋊C4—4716no—
575C22⋊C4—1884no—
576C22⋊C4Dic47⋊C4116yescomplemented
577C42—9416no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—22no—
590C23—24no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23C4⋊C4×D4714yes—
595C23C4⋊C4×D4714yes—
596C23C2×Dic47⋊C414yes—
597C23#1309402014yes—
598C23#1309402214yes—
599C23#1309402314yes—
600C23#1309402314yes—
601C23C22×C4×D4711yescharacteristic
602C23C2×D4×D4711yescharacteristic
603C23C2×D4×D4712yes—
604C23C2×D4×D4711yescharacteristic
605C23C22×C22⋊D4711yescharacteristic
606C23C2×Q8×D4711yescharacteristic
607C23C2×Q8×D4711yescharacteristic
608C23C22×Dic9411yescharacteristic
609C23#41×D4712yes—
610C23#1309406912yes—
611C23#1309407112yes—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—416no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—474no—
637C2×C4—478no—
638C2×C4—474no—
639C2×C4—478no—
640C2×C4—474no—
641C2×C4—474no—
642C2×C4—478no—
643C2×C4—9432no—
644C2×C4—944no—
645C2×C4—944no—
646C2×C4—944no—
647C2×C4—944no—
648C2×C4—944no—
649C2×C4—944no—
650C2×C4—944no—
651C2×C4—942no—
652C2×C4—944no—
653C2×C4—942no—
654C2×C4—944no—
655C2×C4—944no—
656C2×C4—944no—
657C2×C4—1882no—
658C2×C4—1882no—
659C2×C4—1882no—
660C2×C4—1882no—
661C2×C4—1881no—
662C2×C4—1881no—
663C2×C4—1881no—
664C2×C4—1881no—
665C2×C4—1881no—
666C2×C4—1881no—
667C2×C4—18816no—
668C2×C4—1882no—
669C2×C4—1882no—
670C2×C4—1882no—
671C2×C4—1882no—
672C2×C4C2×Dic47⋊C418yescomplemented
673C22—28no—
674C22—28no—
675C22—24no—
676C22—28no—
677C22—28no—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22#1568899218yescomplemented
684C22C2×C4⋊C4×D4711yescharacteristic
685C22C2×C4⋊C4×D4711yescharacteristic
686C22C22×Dic47⋊C411yescharacteristic
687C22C4×D4×D4712yes—
688C22#1568960212yes—
689C22#120×D4711yescharacteristic
690C22C22⋊Q8×D4712yes—
691C22#123×D4711yescharacteristic
692C22C2×#1309402011yescharacteristic
693C22C2×#1309402211yescharacteristic
694C22C2×#1309402311yescharacteristic
695C22C2×#1309402311yescharacteristic
696C22#1568968811yescharacteristic
697C22#1568969511yescharacteristic
698C22#1568975212yes—
699C22#1568975512yes—
700C22D4×C22⋊D4712yes—
701C22#1568977112yes—
702C22#1568977212yes—
703C22#1568978612yes—
704C22D4×Dic9412yes—
705C22#1568982712yes—
706C22#1568983212yes—
707C4—28no—
708C4—44no—
709C4—81no—
710C4—81no—
711C4—478no—
712C4—948no—
713C4—944no—
714C4—3761no—
715C4—3761no—
716C4—1884no—
717C2—28no—
718C2C2×#1568899211yescharacteristic
719C2#385×D4711yescharacteristic
720C2#2024600711yescharacteristic
721C2D4×Dic47⋊C412yes—
722C2#2024628612yes—
723C2#2024702311yescharacteristic
724C2#2024703011yescharacteristic
725C2#2024708712yes—
726C2#2024708912yes—
727C2#2024785711yescharacteristic
728C2#2024786411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#385C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#385D47
hypocenterC47#13880
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
5. C2×#15688992C2semidirect
8. #20241652C2semidirect
9. #20241651C2semidirect
10. Dic47⋊#95C2semidirect
31. C22⋊C4×Dic47C4semidirect
88. C2×C4×Dic47C2×C4semidirect
94. C47⋊#95C2×C4semidirect
187. C22×Dic47C4⋊C4semidirect
202. C22⋊C4×C47C4⋊C4semidirect
204. C22⋊Dic47C4⋊C4semidirect
271. C2×C4×C47C2×C4⋊C4semidirect
303. C2×Dic47C2×C4⋊C4semidirect
319. C22×C47#384semidirect
352. Dic47#385semidirect
408. C47#13880semidirect
576. C22⋊C4Dic47⋊C4semidirect
672. C2×C4C2×Dic47⋊C4semidirect
683. C22#15688992semidirect

Maximal subgroups

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

subgroupindex
C23×Dic47⋊C42
C2×#156889982
C2×#156889962
C2×#156889952
C2×#156889922
C2×#156889812
C2×C22⋊C4×Dic472
#202416522
#202416512
Dic47⋊#952
C2×C47×#3852
#1388047