Finite Group Databasebeta

← #26152986

Subgroups — #26152986

Order 12032.

1934 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094022C211yesmaximal, characteristic
2C2×#15689044C211yesmaximal, characteristic
3C2×#15689043C211yesmaximal, characteristic
4C2×#15689042C211yesmaximal, characteristic
5C2×#15689018C211yesmaximal, characteristic
6C2×#15688992C212yesmaximal
7#20241652C212yesmaximal
8#20241651C212yesmaximal
9Dic47⋊#95C212yesmaximal
10#95×Dic47C211yesmaximal, characteristic
11C2×C47×#395C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C2×#13094022—28no—
14C2×#13094022—24no—
15C22×C4⋊Dic47C2212yes—
16C22×Dic47⋊C4C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×Dic47⋊C4C2212yes—
20C22×Dic47⋊C4C2212yes—
21C22×Dic47⋊C4C2212yes—
22C22×Dic47⋊C4C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2212yes—
25#15689044—24no—
26#15689043—24no—
27#15689042—24no—
28#15689018—24no—
29#15688992—28no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2212yes—
37C23×Q8×C47C2211yescharacteristic
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2212yes—
40C47×#395—24no—
41C2×#95×C47C2212yes—
42C2×#95×C47C2211yescharacteristic
43C22×Dic94—22no—
44C22×Dic94—24no—
45C22×Dic94—22no—
46C22×Dic94—22no—
47C22×Dic94—42no—
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2312yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2312yes—
53C23×Dic47C2311yescharacteristic
54#13094022—232no—
55C2×C4⋊Dic47—24no—
56C2×C4⋊Dic47—24no—
57C2×C4⋊Dic47—42no—
58C2×Dic47⋊C4—24no—
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—22no—
67C2×Dic47⋊C4—22no—
68C2×Dic47⋊C4—22no—
69C2×Dic47⋊C4—24no—
70C2×Dic47⋊C4—24no—
71C2×Dic47⋊C4—22no—
72C2×Dic47⋊C4—24no—
73C2×Dic47⋊C4—24no—
74C2×Dic47⋊C4—42no—
75C2×Dic47⋊C4—42no—
76C2×Dic47⋊C4D418yes—
77C2×Dic47⋊C4Q814yescomplemented
78C2×C4×Dic47—24no—
79C2×C4×Dic47—24no—
80C2×C4×Dic47—24no—
81C2×C4×Dic47D414yes—
82C2×C4×Dic47Q818yescomplemented
83C47⋊#95—24no—
84C47⋊#95—22no—
85C47⋊#95—22no—
86C47⋊#95—24no—
87C47⋊#95—24no—
88C47⋊#95D414yes—
89C47⋊#95Q818yescomplemented
90C22×Q8×C47—24no—
91C22×Q8×C47—22no—
92C22×Q8×C47—22no—
93C22×Q8×C47—22no—
94C22×Q8×C47—42no—
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2312yes—
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2312yes—
100C2×C4⋊C4×C47—24no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—24no—
104C2×C4⋊C4×C47—22no—
105C2×C4⋊C4×C47—42no—
106#95×C47—24no—
107#95×C47D414yes—
108C24×C47C2411yescharacteristic
109C2×Q8×C47—28no—
110C2×Q8×C47—48no—
111C2×Q8×C47—48no—
112C2×Q8×C47—44no—
113C2×Q8×C47—44no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—21no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—22no—
135C22×C4×C47—21no—
136C22×C4×C47—22no—
137C22×C4×C47C2×D414yes—
138C22×C4×C47C2×D412yes—
139C22×C4×C47C2×D412yes—
140C22×C4×C47C2×D412yes—
141C22×C4×C47C2×D414yes—
142C22×C4×C47C2×Q812yes—
143C22×C4×C47C2×Q814yes—
144C22×C4×C47C2×Q814yes—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—22no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—21no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—22no—
167C22×Dic47—21no—
168C22×Dic47—22no—
169C22×Dic47C2×D414yes—
170C22×Dic47C2×D412yes—
171C22×Dic47C2×D414yes—
172C22×Dic47C2×D414yes—
173C22×Dic47C2×D412yes—
174C22×Dic47C2×Q812yes—
175C22×Dic47C2×Q814yes—
176C22×Dic47C2×Q814yes—
177C22×Dic47C2×Q814yes—
178C22×Dic47C2×Q814yes—
179C22×Dic47C2×Q812yes—
180C22×Dic47#4112yes—
181C2×Dic94—28no—
182C2×Dic94—48no—
183C2×Dic94—48no—
184C2×Dic94—44no—
185C2×Dic94—44no—
186C4⋊C4×C47—48no—
187C4⋊C4×C47—44no—
188C4⋊Dic47—48no—
189Dic47⋊C4—216no—
190Dic47⋊C4—216no—
191Dic47⋊C4—28no—
192Dic47⋊C4—48no—
193Dic47⋊C4—48no—
194Dic47⋊C4—44no—
195Dic47⋊C4—44no—
196C4×Dic47—28no—
197C4×Dic47—216no—
198C23×C47C22×D411yescharacteristic
199C23×C47C22×D412yes—
200C23×C47C22×D411yescharacteristic
201C23×C47C22×D411yescharacteristic
202C23×C47C22×Q812yes—
203C23×C47C22×Q811yescharacteristic
204C23×C47C22×Q812yes—
205C23×C47C2×#4111yescharacteristic
206C23×C47H(5,𝔽2)12yes—
207C23×C472−1+411yescharacteristic
208C23×C472−1+411yescharacteristic
209Q8×C47—416no—
210C2×C4×C47—22no—
211C2×C4×C47—24no—
212C2×C4×C47—22no—
213C2×C4×C47—24no—
214C2×C4×C47—24no—
215C2×C4×C47—24no—
216C2×C4×C47—24no—
217C2×C4×C47—24no—
218C2×C4×C47—24no—
219C2×C4×C47—24no—
220C2×C4×C47—24no—
221C2×C4×C47—22no—
222C2×C4×C47—24no—
223C2×C4×C47—24no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—41no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47—41no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47#12714yes—
240C2×C4×C47C4⋊Q818yescomplemented
241C2×Dic47—22no—
242C2×Dic47—24no—
243C2×Dic47—22no—
244C2×Dic47—24no—
245C2×Dic47—24no—
246C2×Dic47—24no—
247C2×Dic47—24no—
248C2×Dic47—24no—
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—22no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—41no—
258C2×Dic47—42no—
259C2×Dic47—42no—
260C2×Dic47—41no—
261C2×Dic47—42no—
262C2×Dic47—42no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—42no—
269C2×Dic47—42no—
270C2×Dic47#12014yes—
271C2×Dic47C22⋊Q818yes—
272C2×Dic47C22⋊Q814yes—
273C2×Dic47C4⋊Q814yes—
274C2×Dic47C4⋊Q814yes—
275C2×Dic47C4⋊Q818yes—
276C2×Dic47C4⋊Q818yescomplemented
277Dic94—416no—
278#15143—471nomaximal, Sylow
279C22×C47C2×#12011yescharacteristic
280C22×C47C2×C22⋊Q811yescharacteristic
281C22×C47C2×C22⋊Q812yes—
282C22×C47C2×#12711yescharacteristic
283C22×C47C2×C4⋊Q811yescharacteristic
284C22×C47C2×C4⋊Q811yescharacteristic
285C22×C47C2×C4⋊Q812yes—
286C22×C47C2×C4⋊Q812yes—
287C22×C47C2×C4⋊Q812yes—
288C22×C47#53511yescharacteristic
289C22×C47#53611yescharacteristic
290C22×C47#54412yes—
291C22×C47#54412yes—
292C22×C47D4212yes—
293C22×C47D4212yes—
294C22×C47#54711yescharacteristic
295C22×C47#54711yescharacteristic
296C22×C47D4×Q812yes—
297C22×C47D4×Q811yescharacteristic
298C22×C47D4×Q811yescharacteristic
299C22×C47D4×Q812yes—
300C22×C47#55412yes—
301C22×C47Q8212yes—
302C4×C47—24no—
303C4×C47—28no—
304C4×C47—44no—
305C4×C47—42no—
306C4×C47—81no—
307Dic47—24no—
308Dic47—28no—
309Dic47—44no—
310Dic47—42no—
311Dic47—81no—
312Dic47#39518yescomplemented
313C22×C4⋊Q8—471no—
314C2×#395—471no—
315C2×#395—471no—
316C2×#395—471no—
317C2×#395D4711yescharacteristic
318C2×#389—471no—
319C2×#384—472no—
320#1444—472no—
321#1444—472no—
322C4⋊#95—472no—
323C4×#95—471no—
324C2×C47C2×#39511yescharacteristic
325C2×C47#243311yescharacteristic
326C2×C47#243411yescharacteristic
327C2×C47#244012yes—
328C2×C47#244012yes—
329C2×C47#254211yescharacteristic
330C2×C47#255112yes—
331C2×C47#255112yes—
332C2×C47#256711yescharacteristic
333C2×C47#266011yescharacteristic
334C2×C47#286811yescharacteristic
335C23×Q8—471no—
336C23×Q8C2×D4711yescharacteristic
337C2×C4⋊Q8—944no—
338C2×C4⋊Q8—948no—
339C22×C4⋊C4—472no—
340C22×C4⋊C4—471no—
341C22×C4⋊C4—471no—
342C22×C4⋊C4—472no—
343C22×C4⋊C4—471no—
344C22×C4⋊C4—472no—
345C22×C4⋊C4—472no—
346C22×C4⋊C4—472no—
347C22×C4⋊C4C2×D4711yescharacteristic
348C22×C4⋊C4C2×D4712yes—
349C22×C42—471no—
350C22×C42—472no—
351#395—24no—
352#395—944no—
353#395—944no—
354#395—944no—
355#389—944no—
356#384—948no—
357C2×#95—471no—
358C2×#95—472no—
359C2×#95—472no—
360C2×#95—472no—
361C2×#95—472no—
362C2×#95—471no—
363C2×#95—471no—
364C2×#95C2×D4712yes—
365C2×#95C2×D4711yescharacteristic
366C47#1514311yescharacteristic, complemented, Sylow
367C22×Q8—24no—
368C22×Q8—22no—
369C22×Q8—22no—
370C22×Q8—22no—
371C22×Q8—42no—
372C22×Q8—944no—
373C22×Q8—942no—
374C22×Q8—942no—
375C22×Q8—942no—
376C22×Q8—1882no—
377C23×C4—471no—
378C23×C4—472no—
379C23×C4—471no—
380C23×C4—472no—
381C23×C4—471no—
382C23×C4—471no—
383C23×C4C22×D4711yescharacteristic
384C23×C4C22×D4712yes—
385C23×C4C22×D4711yescharacteristic
386C23×C4C22×D4711yescharacteristic
387C23×C4C22×D4712yes—
388C4⋊Q8—9432no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—478no—
396C2×C4⋊C4—474no—
397C2×C4⋊C4—944no—
398C2×C4⋊C4—944no—
399C2×C4⋊C4—944no—
400C2×C4⋊C4—944no—
401C2×C4⋊C4—942no—
402C2×C4⋊C4—942no—
403C2×C4⋊C4—944no—
404C2×C4⋊C4—944no—
405C2×C4⋊C4—944no—
406C2×C4⋊C4—942no—
407C2×C4⋊C4—944no—
408C2×C4⋊C4—944no—
409C2×C4⋊C4—944no—
410C2×C4⋊C4—944no—
411C2×C4⋊C4—942no—
412C2×C4⋊C4—942no—
413C2×C4⋊C4—942no—
414C2×C4⋊C4—944no—
415C2×C4⋊C4—1882no—
416C2×C4⋊C4—1882no—
417C2×C4⋊C4—1882no—
418C2×C42—474no—
419C2×C42—478no—
420C2×C42—944no—
421C2×C42—944no—
422C2×C42—944no—
423#95—24no—
424#95—474no—
425#95—478no—
426#95—942no—
427#95—942no—
428#95—944no—
429#95—944no—
430#95—944no—
431#95C22⋊D4714yes—
432C24C23×D4711yescharacteristic
433C2×Q8—28no—
434C2×Q8—48no—
435C2×Q8—48no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×Q8—948no—
439C2×Q8—1888no—
440C2×Q8—1888no—
441C2×Q8—1884no—
442C2×Q8—1884no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—472no—
467C22×C4—474no—
468C22×C4—474no—
469C22×C4—472no—
470C22×C4—472no—
471C22×C4—474no—
472C22×C4—472no—
473C22×C4—474no—
474C22×C4—474no—
475C22×C4—474no—
476C22×C4—474no—
477C22×C4—472no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—941no—
483C22×C4—942no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—941no—
491C22×C4—942no—
492C22×C4—941no—
493C22×C4—942no—
494C22×C4—942no—
495C22×C4—941no—
496C22×C4—941no—
497C22×C4—941no—
498C22×C4—941no—
499C22×C4—942no—
500C22×C4—941no—
501C22×C4—942no—
502C22×C4D4×D4714yes—
503C22×C4D4×D4712yes—
504C22×C4D4×D4712yes—
505C22×C4Q8×D4712yes—
506C22×C4Q8×D4714yes—
507C22×C4Q8×D4714yes—
508C22×C4C2×C22⋊D4712yes—
509C22×C4C2×C22⋊D4714yes—
510C4⋊C4—48no—
511C4⋊C4—44no—
512C4⋊C4—948no—
513C4⋊C4—9416no—
514C4⋊C4—9416no—
515C4⋊C4—1888no—
516C4⋊C4—1888no—
517C4⋊C4—1884no—
518C4⋊C4—1888no—
519C4⋊C4—1884no—
520C42—9416no—
521C42—948no—
522C23C2×D4×D4711yescharacteristic
523C23C2×D4×D4712yes—
524C23C2×D4×D4711yescharacteristic
525C23C22×C22⋊D4711yescharacteristic
526C23C2×Q8×D4712yes—
527C23C2×Q8×D4711yescharacteristic
528C23C2×Q8×D4712yes—
529C23#41×D4711yescharacteristic
530C23#1309406912yes—
531C23#1309407111yescharacteristic
532C23#1309407211yescharacteristic
533Q8—416no—
534Q8—18816no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—474no—
565C2×C4—478no—
566C2×C4—474no—
567C2×C4—478no—
568C2×C4—474no—
569C2×C4—474no—
570C2×C4—478no—
571C2×C4—944no—
572C2×C4—944no—
573C2×C4—944no—
574C2×C4—944no—
575C2×C4—944no—
576C2×C4—944no—
577C2×C4—944no—
578C2×C4—942no—
579C2×C4—944no—
580C2×C4—942no—
581C2×C4—944no—
582C2×C4—944no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—944no—
586C2×C4—942no—
587C2×C4—1882no—
588C2×C4—1882no—
589C2×C4—1881no—
590C2×C4—1881no—
591C2×C4—1881no—
592C2×C4—1882no—
593C2×C4—1882no—
594C2×C4—1881no—
595C2×C4—1881no—
596C2×C4—1881no—
597C2×C4—1882no—
598C2×C4—1882no—
599C2×C4—1881no—
600C2×C4#1309402014yes—
601C2×C4#1309402218yescomplemented
602C22#120×D4711yescharacteristic
603C22C22⋊Q8×D4711yescharacteristic
604C22C22⋊Q8×D4712yes—
605C22C2×#1309402011yescharacteristic
606C22C4⋊Q8×D4711yescharacteristic
607C22C4⋊Q8×D4712yes—
608C22C4⋊Q8×D4712yes—
609C22C4⋊Q8×D4711yescharacteristic
610C22C2×#1309402212yes—
611C22#1568968811yescharacteristic
612C22#1568969611yescharacteristic
613C22#1568975012yes—
614C22#1568975212yes—
615C22#1568975512yes—
616C22D4×C22⋊D4712yes—
617C22#1568977211yescharacteristic
618C22#1568977511yescharacteristic
619C22#1568978611yescharacteristic
620C22#1568978612yes—
621C22Q8×C22⋊D4711yescharacteristic
622C22#1568978812yes—
623C22#1568982712yes—
624C22#1568985312yes—
625C4—28no—
626C4—24no—
627C4—42no—
628C4—44no—
629C4—81no—
630C4—478no—
631C4—948no—
632C4—944no—
633C4—3761no—
634C4—1882no—
635C4—1884no—
636C2#395×D4711yescharacteristic
637C2#2024702311yescharacteristic
638C2#2024702711yescharacteristic
639C2#2024708312yes—
640C2#2024708712yes—
641C2#2024833811yescharacteristic
642C2#2024841312yes—
643C2#2024841512yes—
644C2#2024859211yescharacteristic
645C2#2024950611yescharacteristic
646C2#2025178411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, prime radical, cosocleC24×C47C24
FittingC2×C47×#395C2
hypercenterC2×#395D47
hypocenterC47#15143
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
77. C2×Dic47⋊C4Q8semidirect
82. C2×C4×Dic47Q8semidirect
89. C47⋊#95Q8semidirect
240. C2×C4×C47C4⋊Q8semidirect
276. C2×Dic47C4⋊Q8semidirect
312. Dic47#395semidirect
366. C47#15143semidirect
601. C2×C4#13094022semidirect

Maximal subgroups

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

subgroupindex
C22×#130940222
C2×#156890442
C2×#156890432
C2×#156890422
C2×#156890182
C2×#156889922
#202416522
#202416512
Dic47⋊#952
#95×Dic472
C2×C47×#3952
#1514347