Finite Group Databasebeta

← #26153000

Subgroups — #26153000

Order 12032.

1566 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689055C211yesmaximal, characteristic
2C2×#15689054C211yesmaximal, characteristic
3C2×#15689053C211yesmaximal, characteristic
4C2×#15689018C211yesmaximal, characteristic
5C2×#15688992C212yesmaximal
6C2×#15688992C211yesmaximal, characteristic
7#20241652C212yesmaximal
8#20241651C212yesmaximal
9Dic47⋊#95C212yesmaximal
10#95×Dic47C211yesmaximal, characteristic
11C2×C47×#398C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×Dic47⋊C4C2212yes—
15C22×Dic47⋊C4C2211yescharacteristic
16C22×Dic47⋊C4C2211yescharacteristic
17C22×Dic47⋊C4C2212yes—
18C22×Dic47⋊C4C2212yes—
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2212yes—
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2212yes—
23#15689055—24no—
24#15689054—24no—
25#15689053—24no—
26#15689018—24no—
27#15688992—28no—
28#15688992—24no—
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2212yes—
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C4⋊C4×C47C2212yes—
39C47×#398—24no—
40C2×#95×C47C2212yes—
41C2×#95×C47C2211yescharacteristic
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2312yes—
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C23×Dic47C2311yescharacteristic
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—24no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—24no—
53C2×C4⋊Dic47—42no—
54C2×Dic47⋊C4—22no—
55C2×Dic47⋊C4—22no—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—24no—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4—24no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—22no—
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4—24no—
69C2×Dic47⋊C4—42no—
70C2×Dic47⋊C4—42no—
71C2×Dic47⋊C4—42no—
72C2×Dic47⋊C4—42no—
73C2×Dic47⋊C4D414yes—
74C2×C4×Dic47—24no—
75C2×C4×Dic47—24no—
76C2×C4×Dic47—24no—
77C2×C4×Dic47D414yes—
78C2×C4×Dic47Q818yes—
79C47⋊#95—24no—
80C47⋊#95—22no—
81C47⋊#95—22no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95D414yes—
85C47⋊#95Q818yes—
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2312yes—
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2312yes—
91C2×C4⋊C4×C47—24no—
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47—22no—
94C2×C4⋊C4×C47—22no—
95C2×C4⋊C4×C47—22no—
96C2×C4⋊C4×C47—24no—
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47—22no—
99C2×C4⋊C4×C47—42no—
100#95×C47—24no—
101#95×C47D414yes—
102C24×C47C2411yescharacteristic
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
115C22×C4×C47—22no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—21no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47C2×D412yes—
128C22×C4×C47C2×D412yes—
129C22×C4×C47C2×D412yes—
130C22×C4×C47C2×D412yes—
131C22×C4×C47C2×D414yes—
132C22×C4×C47C2×Q814yes—
133C22×C4×C47C2×Q814yes—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47C2×D412yes—
160C22×Dic47C2×D414yes—
161C22×Dic47C2×D412yes—
162C22×Dic47C2×D412yes—
163C22×Dic47C2×D412yes—
164C22×Dic47C2×Q814yes—
165C22×Dic47C2×Q814yes—
166C22×Dic47C2×Q814yes—
167C22×Dic47C2×Q814yes—
168C22×Dic47#4112yes—
169C22×Dic47#4114yes—
170C4⋊C4×C47—48no—
171C4⋊C4×C47—44no—
172C4⋊C4×C47—44no—
173C4⋊Dic47—48no—
174C4⋊Dic47—44no—
175Dic47⋊C4—28no—
176Dic47⋊C4—48no—
177Dic47⋊C4—48no—
178Dic47⋊C4—48no—
179Dic47⋊C4—44no—
180Dic47⋊C4—48no—
181Dic47⋊C4—44no—
182C4×Dic47—216no—
183C4×Dic47—28no—
184C23×C47C22×D411yescharacteristic
185C23×C47C22×D411yescharacteristic
186C23×C47C22×D411yescharacteristic
187C23×C47C22×D411yescharacteristic
188C23×C47C22×Q812yes—
189C23×C47C22×Q812yes—
190C23×C47C2×#4111yescharacteristic
191C23×C47C2×#4112yes—
192C23×C47H(5,𝔽2)11yescharacteristic
193C23×C47H(5,𝔽2)11yescharacteristic
194C23×C472−1+412yes—
195C2×C4×C47—24no—
196C2×C4×C47—22no—
197C2×C4×C47—22no—
198C2×C4×C47—24no—
199C2×C4×C47—24no—
200C2×C4×C47—24no—
201C2×C4×C47—24no—
202C2×C4×C47—24no—
203C2×C4×C47—24no—
204C2×C4×C47—24no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—41no—
212C2×C4×C47—42no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—41no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47#12714yes—
225C2×C4×C47C4⋊Q818yes—
226C2×Dic47—24no—
227C2×Dic47—22no—
228C2×Dic47—22no—
229C2×Dic47—24no—
230C2×Dic47—24no—
231C2×Dic47—24no—
232C2×Dic47—24no—
233C2×Dic47—24no—
234C2×Dic47—24no—
235C2×Dic47—24no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—42no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—41no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47#12114yes—
256C2×Dic47C22⋊Q818yes—
257C2×Dic47#12314yes—
258C2×Dic47#12518yes—
259C2×Dic47C4⋊Q818yes—
260C2×Dic47C4⋊Q814yes—
261C2×Dic47C4⋊Q814yes—
262#15145—471nomaximal, Sylow
263C22×C47C2×#12111yescharacteristic
264C22×C47C2×C22⋊Q812yes—
265C22×C47C2×#12311yescharacteristic
266C22×C47C2×#12512yes—
267C22×C47C2×#12711yescharacteristic
268C22×C47C2×C4⋊Q811yescharacteristic
269C22×C47C2×C4⋊Q812yes—
270C22×C47C2×C4⋊Q811yescharacteristic
271C22×C47C2×C4⋊Q812yes—
272C22×C47#53511yescharacteristic
273C22×C47#53611yescharacteristic
274C22×C47#54412yes—
275C22×C47#54412yes—
276C22×C47D4211yescharacteristic
277C22×C47D4211yescharacteristic
278C22×C47#54712yes—
279C22×C47#54712yes—
280C22×C47D4×Q812yes—
281C22×C47#55011yescharacteristic
282C22×C47#55011yescharacteristic
283C22×C47#55412yes—
284C22×C47#55412yes—
285C22×C47#55712yes—
286C4×C47—28no—
287C4×C47—24no—
288C4×C47—42no—
289C4×C47—81no—
290C4×C47—82no—
291Dic47—28no—
292Dic47—24no—
293Dic47—42no—
294Dic47—81no—
295Dic47—82no—
296Dic47#39818yescomplemented
297C2×#398—471no—
298C2×#398—471no—
299C2×#398—471no—
300C2×#398D4711yescharacteristic
301C2×#389—471no—
302C2×#384—472no—
303C2×#384—471no—
304#1444—472no—
305#1444—472no—
306C4⋊#95—472no—
307C4×#95—471no—
308C2×C47C2×#39811yescharacteristic
309C2×C47#244012yes—
310C2×C47#244012yes—
311C2×C47#250111yescharacteristic
312C2×C47#250211yescharacteristic
313C2×C47#254111yescharacteristic
314C2×C47#254611yescharacteristic
315C2×C47#255212yes—
316C2×C47#255212yes—
317C2×C47#266011yescharacteristic
318C2×C47#286811yescharacteristic
319C22×C4⋊C4—471no—
320C22×C4⋊C4—471no—
321C22×C4⋊C4—471no—
322C22×C4⋊C4—471no—
323C22×C4⋊C4—472no—
324C22×C4⋊C4—472no—
325C22×C4⋊C4—472no—
326C22×C4⋊C4—472no—
327C22×C4⋊C4—472no—
328C22×C4⋊C4C2×D4711yescharacteristic
329C22×C4⋊C4C2×D4711yescharacteristic
330C22×C4⋊C4C2×D4712yes—
331C22×C42—472no—
332C22×C42—471no—
333#398—24no—
334#398—944no—
335#398—944no—
336#398—944no—
337#389—944no—
338#384—944no—
339#384—948no—
340C2×#95—471no—
341C2×#95—472no—
342C2×#95—472no—
343C2×#95—472no—
344C2×#95—472no—
345C2×#95—471no—
346C2×#95—471no—
347C2×#95C2×D4712yes—
348C2×#95C2×D4711yescharacteristic
349C47#1514511yescharacteristic, complemented, Sylow
350C23×C4—471no—
351C23×C4—472no—
352C23×C4—471no—
353C23×C4—471no—
354C23×C4—472no—
355C23×C4—471no—
356C23×C4C22×D4712yes—
357C23×C4C22×D4711yescharacteristic
358C23×C4C22×D4711yescharacteristic
359C23×C4C22×D4711yescharacteristic
360C23×C4C22×D4712yes—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—474no—
371C2×C4⋊C4—942no—
372C2×C4⋊C4—942no—
373C2×C4⋊C4—944no—
374C2×C4⋊C4—944no—
375C2×C4⋊C4—944no—
376C2×C4⋊C4—944no—
377C2×C4⋊C4—944no—
378C2×C4⋊C4—944no—
379C2×C4⋊C4—942no—
380C2×C4⋊C4—944no—
381C2×C4⋊C4—944no—
382C2×C4⋊C4—944no—
383C2×C4⋊C4—944no—
384C2×C4⋊C4—942no—
385C2×C4⋊C4—942no—
386C2×C4⋊C4—942no—
387C2×C4⋊C4—942no—
388C2×C4⋊C4—942no—
389C2×C4⋊C4—944no—
390C2×C4⋊C4—942no—
391C2×C4⋊C4—1882no—
392C2×C4⋊C4—1882no—
393C2×C4⋊C4—1882no—
394C2×C4⋊C4—1882no—
395C2×C4⋊C4—1882no—
396C2×C42—474no—
397C2×C42—478no—
398C2×C42—944no—
399C2×C42—944no—
400C2×C42—944no—
401#95—24no—
402#95—474no—
403#95—478no—
404#95—942no—
405#95—942no—
406#95—944no—
407#95—944no—
408#95—944no—
409#95C22⋊D4714yes—
410C24C23×D4711yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—472no—
436C22×C4—472no—
437C22×C4—474no—
438C22×C4—474no—
439C22×C4—472no—
440C22×C4—474no—
441C22×C4—472no—
442C22×C4—474no—
443C22×C4—474no—
444C22×C4—474no—
445C22×C4—472no—
446C22×C4—942no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—941no—
450C22×C4—942no—
451C22×C4—941no—
452C22×C4—942no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—942no—
461C22×C4—941no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—941no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4D4×D4712yes—
472C22×C4D4×D4712yes—
473C22×C4D4×D4712yes—
474C22×C4Q8×D4714yes—
475C22×C4Q8×D4714yes—
476C22×C4C2×C22⋊D4712yes—
477C22×C4C2×C22⋊D4714yes—
478C4⋊C4—48no—
479C4⋊C4—44no—
480C4⋊C4—44no—
481C4⋊C4—948no—
482C4⋊C4—1888no—
483C4⋊C4—1888no—
484C4⋊C4—1888no—
485C4⋊C4—1884no—
486C4⋊C4—1888no—
487C4⋊C4—1888no—
488C4⋊C4—1884no—
489C4⋊C4—1884no—
490C42—9416no—
491C42—948no—
492C23C2×D4×D4711yescharacteristic
493C23C2×D4×D4711yescharacteristic
494C23C2×D4×D4711yescharacteristic
495C23C22×C22⋊D4711yescharacteristic
496C23C2×Q8×D4712yes—
497C23C2×Q8×D4712yes—
498C23#41×D4712yes—
499C23#41×D4711yescharacteristic
500C23#1309406911yescharacteristic
501C23#1309407011yescharacteristic
502C23#1309407112yes—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—474no—
533C2×C4—478no—
534C2×C4—474no—
535C2×C4—478no—
536C2×C4—474no—
537C2×C4—478no—
538C2×C4—474no—
539C2×C4—944no—
540C2×C4—944no—
541C2×C4—944no—
542C2×C4—944no—
543C2×C4—944no—
544C2×C4—944no—
545C2×C4—944no—
546C2×C4—944no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4—1882no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4—1881no—
560C2×C4—1882no—
561C2×C4—1881no—
562C2×C4—1882no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4#1309402014yes—
569C2×C4#1309402218yes—
570C22#121×D4711yescharacteristic
571C22C22⋊Q8×D4712yes—
572C22#123×D4711yescharacteristic
573C22#125×D4712yes—
574C22C2×#1309402011yescharacteristic
575C22C4⋊Q8×D4712yes—
576C22C4⋊Q8×D4711yescharacteristic
577C22C4⋊Q8×D4711yescharacteristic
578C22C2×#1309402212yes—
579C22#1568968911yescharacteristic
580C22#1568969511yescharacteristic
581C22#1568975212yes—
582C22#1568975312yes—
583C22D4×C22⋊D4711yescharacteristic
584C22#1568975711yescharacteristic
585C22#1568977112yes—
586C22#1568977212yes—
587C22#1568978612yes—
588C22#1568979111yescharacteristic
589C22#1568979211yescharacteristic
590C22#1568982712yes—
591C22#1568982912yes—
592C22#1568985012yes—
593C4—28no—
594C4—24no—
595C4—42no—
596C4—82no—
597C4—81no—
598C4—478no—
599C4—948no—
600C4—944no—
601C4—3762no—
602C4—3761no—
603C4—1882no—
604C2#398×D4711yescharacteristic
605C2#2024708512yes—
606C2#2024708712yes—
607C2#2024785711yescharacteristic
608C2#2024786111yescharacteristic
609C2#2024833111yescharacteristic
610C2#2024837211yescharacteristic
611C2#2024841812yes—
612C2#2024842012yes—
613C2#2024951111yescharacteristic
614C2#2025178411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, prime radical, cosocleC24×C47C24
FittingC2×C47×#398C2
hypercenterC2×#398D47
hypocenterC47#15145
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
296. Dic47#398semidirect
349. C47#15145semidirect

Maximal subgroups

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

subgroupindex
C2×#156890552
C2×#156890542
C2×#156890532
C2×#156890182
C2×#156889922
#202416522
#202416512
Dic47⋊#952
#95×Dic472
C2×C47×#3982
#1514547