Finite Group Databasebeta

← #26147697

Subgroups — #26147697

Order 12032.

2494 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094001C211yesmaximal, characteristic
2C23×C4⋊Dic47C211yesmaximal, characteristic
3C2×#15689044C212yesmaximal, complemented
4C2×#15688998C211yesmaximal, characteristic
5C2×#15688995C211yesmaximal, characteristic
6#20241653C212yesmaximal, complemented
7#20241652C212yesmaximal, complemented
8#20241640C212yesmaximal, complemented
9#20241611C211yesmaximal, characteristic
10#20241610C211yesmaximal, characteristic
11C47×C22⋊#95C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C24×Dic47C2211yescharacteristic
15C2×#13094001—24no—
16C2×#13094001—24no—
17C2×#13094001—24no—
18C22×C4⋊Dic47—24no—
19C22×C4⋊Dic47—28no—
20C22×C4⋊Dic47C2212yes—
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2212yes—
23C22×C4⋊Dic47C2212yes—
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2212yes—
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29#15689044—28no—
30#15688998—24no—
31#15688995—24no—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C2×C47⋊#95C2212yes—
38C24×C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2211yescharacteristic
40C22×C22⋊C4×C47C2211yescharacteristic
41C2×#95×C47C2212yes—
42C2×#95×C47C2212yes—
43C22×Dic94—22no—
44C22×Dic94—22no—
45C22×Dic94—22no—
46C22×Dic94—24no—
47C22×Dic94—42no—
48C23×Dic47—22no—
49C23×Dic47—22no—
50C23×Dic47—22no—
51C23×Dic47—24no—
52C23×Dic47—24no—
53C23×Dic47—22no—
54C23×Dic47—22no—
55C23×Dic47—42no—
56C23×Dic47—42no—
57C23×Dic47D414yes—
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2312yes—
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2312yes—
63C23×Dic47C2311yescharacteristic
64#13094001—232no—
65C2×C4⋊Dic47—232no—
66C2×C4⋊Dic47—24no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—24no—
69C2×C4⋊Dic47—24no—
70C2×C4⋊Dic47—24no—
71C2×C4⋊Dic47—24no—
72C2×C4⋊Dic47—22no—
73C2×C4⋊Dic47—22no—
74C2×C4⋊Dic47—24no—
75C2×C4⋊Dic47—24no—
76C2×C4⋊Dic47—42no—
77C2×C4⋊Dic47D418yes—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4—22no—
83C2×Dic47⋊C4—22no—
84C2×Dic47⋊C4—24no—
85C2×Dic47⋊C4—24no—
86C2×Dic47⋊C4—42no—
87C2×C22⋊Dic47—22no—
88C2×C22⋊Dic47—22no—
89C2×C22⋊Dic47—22no—
90C2×C22⋊Dic47—22no—
91C2×C22⋊Dic47D414yes—
92C2×C22⋊Dic47Q814yescomplemented
93C47⋊#95—24no—
94C47⋊#95—24no—
95C47⋊#95—24no—
96C47⋊#95—24no—
97C47⋊#95—24no—
98C47⋊#95—42no—
99C25×C47C2311yescharacteristic
100C23×C4×C47—22no—
101C23×C4×C47—22no—
102C23×C4×C47—24no—
103C23×C4×C47—24no—
104C23×C4×C47Q814yescomplemented
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2312yes—
108C23×C4×C47C2312yes—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—22no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47D414yes—
114C2×C22⋊C4×C47Q814yescomplemented
115#95×C47—24no—
116#95×C47—24no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47—22no—
120C24×C47—22no—
121C24×C47C2×D412yes—
122C24×C47C2×D412yes—
123C24×C47C2×D412yes—
124C24×C47C2×Q812yes—
125C24×C47C2×Q812yes—
126C24×C47C2×Q812yes—
127C24×C47#4112yes—
128C24×C47C2411yescharacteristic
129C22×C4×C47—216no—
130C22×C4×C47—28no—
131C22×C4×C47—28no—
132C22×C4×C47—28no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—216no—
138C22×C4×C47—22no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
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×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47C2×D412yes—
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2×D414yes—
155C22×C4×C47C2×Q814yes—
156C22×C4×C47C2×Q814yes—
157C22×C4×C47#4114yes—
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—22no—
161C22×Dic47—28no—
162C22×Dic47—28no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—28no—
188C22×Dic47—44no—
189C22×Dic47—48no—
190C22×Dic47—48no—
191C22×Dic47—48no—
192C22×Dic47—48no—
193C22×Dic47—44no—
194C22×Dic47—44no—
195C22×Dic47C2×D412yes—
196C22×Dic47C2×D412yes—
197C22×Dic47C2×D412yes—
198C22×Dic47C2×D414yes—
199C22×Dic47C2×D414yes—
200C22×Dic47C2×D412yes—
201C22×Dic47C2×Q814yes—
202C2×Dic94—28no—
203C2×Dic94—48no—
204C2×Dic94—48no—
205C2×Dic94—44no—
206C2×Dic94—44no—
207C22⋊C4×C47—28no—
208C22⋊C4×C47—28no—
209C22⋊Dic47—28no—
210C22⋊Dic47—28no—
211C4⋊Dic47—216no—
212C4⋊Dic47—28no—
213C4⋊Dic47—216no—
214C4⋊Dic47—48no—
215Dic47⋊C4—28no—
216Dic47⋊C4—28no—
217Dic47⋊C4—48no—
218C23×C47—22no—
219C23×C47—24no—
220C23×C47—22no—
221C23×C47—24no—
222C23×C47—22no—
223C23×C47—22no—
224C23×C47—24no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—24no—
228C23×C47—24no—
229C23×C47—24no—
230C23×C47—24no—
231C23×C47—24no—
232C23×C47—24no—
233C23×C47—24no—
234C23×C47#12014yes—
235C23×C47C22⋊Q814yes—
236C23×C47C22⋊Q814yes—
237C23×C47C22⋊Q814yes—
238C23×C47C4⋊Q814yes—
239C23×C47C4⋊Q814yes—
240C23×C47C4⋊Q814yes—
241C23×C47C22×D411yescharacteristic
242C23×C47C22×D412yes—
243C23×C47C22×D411yescharacteristic
244C23×C47C22×D411yescharacteristic
245C23×C47C22×Q811yescharacteristic
246C23×C47C22×Q811yescharacteristic
247C23×C47C22×Q811yescharacteristic
248C23×C47C2×#4111yescharacteristic
249C23×C47C2×#4112yes—
250C23×C47H(5,𝔽2)12yes—
251C23×C472−1+412yes—
252C2×C4×C47—232no—
253C2×C4×C47—24no—
254C2×C4×C47—24no—
255C2×C4×C47—24no—
256C2×C4×C47—24no—
257C2×C4×C47—24no—
258C2×C4×C47—24no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—24no—
262C2×C4×C47—24no—
263C2×C4×C47—24no—
264C2×C4×C47—24no—
265C2×C4×C47—24no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—42no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—42no—
272C2×C4×C47—42no—
273C2×C4×C47—42no—
274C2×C4×C47—42no—
275C2×C4×C47—42no—
276C2×C4×C47C22⋊Q818yescomplemented
277C2×Dic47—22no—
278C2×Dic47—22no—
279C2×Dic47—24no—
280C2×Dic47—24no—
281C2×Dic47—22no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—24no—
285C2×Dic47—22no—
286C2×Dic47—24no—
287C2×Dic47—22no—
288C2×Dic47—24no—
289C2×Dic47—24no—
290C2×Dic47—24no—
291C2×Dic47—24no—
292C2×Dic47—24no—
293C2×Dic47—24no—
294C2×Dic47—416no—
295C2×Dic47—416no—
296C2×Dic47—41no—
297C2×Dic47—42no—
298C2×Dic47—41no—
299C2×Dic47—42no—
300C2×Dic47—41no—
301C2×Dic47—42no—
302C2×Dic47—41no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47#12014yes—
313Dic94—416no—
314#14720—471nomaximal, Sylow
315C22×C47—24no—
316C22×C47—24no—
317C22×C47—24no—
318C22×C47—24no—
319C22×C47—24no—
320C22×C47—24no—
321C22×C47—28no—
322C22×C47—28no—
323C22×C47—28no—
324C22×C47—28no—
325C22×C47#39518yescomplemented
326C22×C47C2×#12011yescharacteristic
327C22×C47C2×#12011yescharacteristic
328C22×C47C2×C22⋊Q811yescharacteristic
329C22×C47C2×C22⋊Q812yes—
330C22×C47C2×C22⋊Q811yescharacteristic
331C22×C47C2×C22⋊Q811yescharacteristic
332C22×C47#52511yescharacteristic
333C22×C47#52512yes—
334C22×C47C2×C4⋊Q811yescharacteristic
335C22×C47C2×C4⋊Q811yescharacteristic
336C22×C47C2×C4⋊Q811yescharacteristic
337C22×C47#53411yescharacteristic
338C22×C47#53611yescharacteristic
339C22×C47#53912yes—
340C22×C47#54412yes—
341C22×C47D4212yes—
342C22×C47D4212yes—
343C22×C47#54712yes—
344C22×C47#54712yes—
345C22×C47D4×Q812yes—
346C22×C47D4×Q812yes—
347C22×C47#55412yes—
348C22×C47#55412yes—
349C4×C47—28no—
350C4×C47—42no—
351C4×C47—42no—
352C4×C47—44no—
353Dic47—24no—
354Dic47—42no—
355Dic47—42no—
356Dic47—44no—
357Dic47—42no—
358Dic47—44no—
359C22×C22⋊Q8—471no—
360C23×C4⋊C4—471no—
361C2×#395—472no—
362C2×#385—471no—
363C2×#385—471no—
364#1444—472no—
365#1444—472no—
366#1441—472no—
367C22⋊#95—471no—
368C22⋊#95—471no—
369C22⋊#95D4711yescharacteristic
370C2×C47—28no—
371C2×C47C2×#39511yescharacteristic
372C2×C47#240311yescharacteristic
373C2×C47#240611yescharacteristic
374C2×C47#243411yescharacteristic
375C2×C47#244012yes—
376C2×C47#244012yes—
377C2×C47#244912yes—
378C2×C47#244912yes—
379C2×C47#258311yescharacteristic
380C2×C47#262711yescharacteristic
381C2×C47#284811yescharacteristic
382C23×Q8—471no—
383C24×C4—471no—
384C24×C4—471no—
385C24×C4C2×D4711yescharacteristic
386C2×C22⋊Q8—944no—
387C2×C22⋊Q8—944no—
388C2×C22⋊Q8—944no—
389C22×C4⋊C4—472no—
390C22×C4⋊C4—472no—
391C22×C4⋊C4—471no—
392C22×C4⋊C4—471no—
393C22×C4⋊C4—471no—
394C22×C4⋊C4—472no—
395C22×C4⋊C4—472no—
396C22×C4⋊C4—948no—
397C22×C4⋊C4—944no—
398C22×C22⋊C4—471no—
399C22×C22⋊C4—471no—
400C22×C22⋊C4C2×D4711yescharacteristic
401C22×C22⋊C4C2×D4711yescharacteristic
402#395—948no—
403#385—944no—
404#385—944no—
405C2×#95—472no—
406C2×#95—472no—
407C2×#95—472no—
408C2×#95—472no—
409C2×#95—472no—
410C2×#95—472no—
411C2×#95C2×D4712yes—
412C2×#95C2×D4712yes—
413C47#1472011yescharacteristic, complemented, Sylow
414C25C22×D4711yescharacteristic
415C22×Q8—942no—
416C22×Q8—942no—
417C22×Q8—944no—
418C22×Q8—942no—
419C22×Q8—1882no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—471no—
425C23×C4—471no—
426C23×C4—471no—
427C23×C4—472no—
428C23×C4—472no—
429C23×C4—471no—
430C23×C4—474no—
431C23×C4—944no—
432C23×C4—944no—
433C23×C4—942no—
434C23×C4—942no—
435C23×C4—942no—
436C23×C4—942no—
437C23×C4—942no—
438C23×C4—1882no—
439C23×C4—1882no—
440C23×C4Dic9414yescomplemented
441C23×C4C22×D4712yes—
442C23×C4C22×D4711yescharacteristic
443C23×C4C22×D4711yescharacteristic
444C23×C4C22×D4712yes—
445C22⋊Q8—9432no—
446C2×C4⋊C4—478no—
447C2×C4⋊C4—944no—
448C2×C4⋊C4—944no—
449C2×C4⋊C4—944no—
450C2×C4⋊C4—944no—
451C2×C4⋊C4—942no—
452C2×C4⋊C4—942no—
453C2×C4⋊C4—942no—
454C2×C4⋊C4—942no—
455C2×C4⋊C4—942no—
456C2×C4⋊C4—942no—
457C2×C4⋊C4—9432no—
458C2×C4⋊C4—942no—
459C2×C4⋊C4—942no—
460C2×C4⋊C4—942no—
461C2×C4⋊C4—944no—
462C2×C4⋊C4—944no—
463C2×C4⋊C4—944no—
464C2×C4⋊C4—944no—
465C2×C4⋊C4—944no—
466C2×C4⋊C4—1882no—
467C2×C4⋊C4—1882no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—474no—
473C2×C22⋊C4—474no—
474C2×C22⋊C4—942no—
475C2×C22⋊C4—942no—
476C2×C22⋊C4—942no—
477C2×C22⋊C4—942no—
478C2×C22⋊C4Dic9414yescomplemented
479C2×C22⋊C4D18814yes—
480#95—24no—
481#95—24no—
482#95—944no—
483#95—944no—
484#95—944no—
485#95—944no—
486#95—944no—
487#95—1882no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24C2×Dic9412yes—
493C24C2×Dic9412yes—
494C24C2×D18812yes—
495C24D4×D4712yes—
496C24D4×D4712yes—
497C24#1062535212yes—
498C24Q8×D4712yes—
499C24C23×D4711yescharacteristic
500C2×Q8—948no—
501C2×Q8—1888no—
502C2×Q8—1884no—
503C2×Q8—1888no—
504C2×Q8—1884no—
505C22×C4—28no—
506C22×C4—216no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—216no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—474no—
529C22×C4—472no—
530C22×C4—472no—
531C22×C4—472no—
532C22×C4—474no—
533C22×C4—472no—
534C22×C4—474no—
535C22×C4—948no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—942no—
539C22×C4—948no—
540C22×C4—948no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—941no—
545C22×C4—941no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—941no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
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—942no—
564C22×C4—942no—
565C22×C4—1884no—
566C22×C4—1888no—
567C22×C4—1888no—
568C22×C4—1888no—
569C22×C4—1888no—
570C22×C4—1884no—
571C22×C4—1884no—
572C22×C4C2×Dic9414yes—
573C22×C4C2×Dic9414yes—
574C22×C4C2×D18812yes—
575C22×C4C2×D18812yes—
576C22×C4D4×D4714yes—
577C22×C4#1062535214yes—
578C4⋊C4—9416no—
579C4⋊C4—948no—
580C4⋊C4—948no—
581C4⋊C4—9416no—
582C4⋊C4—948no—
583C4⋊C4—1888no—
584C4⋊C4—1888no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—948no—
588C22⋊C4—948no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—22no—
599C23—24no—
600C23—22no—
601C23—24no—
602C23—22no—
603C23—22no—
604C23—24no—
605C23#1309399414yes—
606C23#1309400114yes—
607C23#1309400114yes—
608C23#1309400414yes—
609C23#1309402314yes—
610C23#1309402314yes—
611C23#1309402414yes—
612C23C2×D4×D4711yescharacteristic
613C23C2×D4×D4712yes—
614C23C2×D4×D4711yescharacteristic
615C23C22×D18811yescharacteristic
616C23C2×Q8×D4711yescharacteristic
617C23C22×Dic9411yescharacteristic
618C23C22×Dic9411yescharacteristic
619C23C2×#1062535212yes—
620C23C2×#1062535211yescharacteristic
621C23#1309407012yes—
622C23#1309407112yes—
623Q8—18816no—
624C2×C4—232no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—474no—
649C2×C4—944no—
650C2×C4—944no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—944no—
654C2×C4—944no—
655C2×C4—944no—
656C2×C4—944no—
657C2×C4—944no—
658C2×C4—944no—
659C2×C4—944no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—944no—
665C2×C4—942no—
666C2×C4—18816no—
667C2×C4—18816no—
668C2×C4—1882no—
669C2×C4—1882no—
670C2×C4—1882no—
671C2×C4—1882no—
672C2×C4—1882no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4—1881no—
677C2×C4—1882no—
678C2×C4—1882no—
679C2×C4—1881no—
680C2×C4—1882no—
681C2×C4—1881no—
682C2×C4—1881no—
683C2×C4—1882no—
684C2×C4#1309400118yescomplemented
685C22—24no—
686C22—28no—
687C22—28no—
688C22—24no—
689C22—28no—
690C22—28no—
691C22—24no—
692C22—24no—
693C22—24no—
694C22—24no—
695C22#1568904418yescomplemented
696C22#120×D4711yescharacteristic
697C22C2×#1309399411yescharacteristic
698C22C2×#1309400112yes—
699C22C2×#1309400111yescharacteristic
700C22C2×#1309400111yescharacteristic
701C22C2×#1309400411yescharacteristic
702C22#1568962912yes—
703C22#1568962911yescharacteristic
704C22C2×#1309402311yescharacteristic
705C22C2×#1309402311yescharacteristic
706C22C2×#1309402411yescharacteristic
707C22#1568968411yescharacteristic
708C22#1568969511yescharacteristic
709C22#1568971712yes—
710C22#1568975112yes—
711C22#1568975712yes—
712C22D4×D18812yes—
713C22#1568977312yes—
714C22#1568977712yes—
715C22#1568978612yes—
716C22D4×Dic9412yes—
717C22#1568983012yes—
718C22#1568983112yes—
719C4—28no—
720C4—44no—
721C4—42no—
722C4—42no—
723C4—944no—
724C4—1884no—
725C4—1884no—
726C4—1882no—
727C4—1882no—
728C4—1882no—
729C2—28no—
730C2C2×#1568904411yescharacteristic
731C2#2024670011yescharacteristic
732C2#2024672211yescharacteristic
733C2#2024703011yescharacteristic
734C2#2024709012yes—
735C2#2024709112yes—
736C2#2024719512yes—
737C2#2024720312yes—
738C2#2024876511yescharacteristic
739C2#2024920511yescharacteristic
740C2#2025167311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, cosocleC24×C47C24
FittingC47×C22⋊#95C2
prime radicalC25×C47C23
hypercenterC22⋊#95D47
hypocenterC47#14720
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#15689044C2semidirect
6. #20241653C2semidirect
7. #20241652C2semidirect
8. #20241640C2semidirect
92. C2×C22⋊Dic47Q8semidirect
104. C23×C4×C47Q8semidirect
114. C2×C22⋊C4×C47Q8semidirect
276. C2×C4×C47C22⋊Q8semidirect
325. C22×C47#395semidirect
413. C47#14720semidirect
440. C23×C4Dic94semidirect
478. C2×C22⋊C4Dic94semidirect
684. C2×C4#13094001semidirect
695. C22#15689044semidirect

Maximal subgroups

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

subgroupindex
C22×#130940012
C23×C4⋊Dic472
C2×#156890442
C2×#156889982
C2×#156889952
#202416532
#202416522
#202416402
#202416112
#202416102
C47×C22⋊#952
#1472047