Finite Group Databasebeta

← #26152989

Subgroups — #26152989

Order 12032.

1934 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094023C211yesmaximal, characteristic
2C2×#15689044C212yesmaximal
3C2×#15689043C212yesmaximal
4C2×#15689020C211yesmaximal, characteristic
5C2×#15688992C212yesmaximal
6#20241653C211yesmaximal, characteristic
7#20241652C211yesmaximal, characteristic
8#20241651C211yesmaximal, characteristic
9Dic47⋊#95C212yesmaximal
10#95×Dic47C211yesmaximal, characteristic
11C47×#1444C211yesmaximal, characteristic
12C23×Dic94C2212yes—
13C2×#13094023—28no—
14C2×#13094023—24no—
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2212yes—
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2212yes—
21C22×Dic47⋊C4C2212yes—
22C22×Dic47⋊C4C2212yes—
23C22×Dic47⋊C4C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2212yes—
26#15689044—28no—
27#15689043—28no—
28#15689020—24no—
29#15688992—28no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C4⋊C4×C47C2212yes—
38C2×#95×C47C2212yes—
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2211yescharacteristic
41C22×Dic94—24no—
42C22×Dic94—24no—
43C22×Dic94—24no—
44C22×Dic94—24no—
45C22×Dic94—24no—
46C22×Dic94—42no—
47C22×Dic94—42no—
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2312yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2312yes—
53C23×Dic47C2311yescharacteristic
54#13094023—232no—
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—24no—
57C2×C4⋊Dic47—24no—
58C2×C4⋊Dic47—24no—
59C2×C4⋊Dic47—22no—
60C2×C4⋊Dic47—24no—
61C2×C4⋊Dic47—42no—
62C2×Dic47⋊C4—22no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—22no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4—24no—
69C2×Dic47⋊C4—22no—
70C2×Dic47⋊C4—22no—
71C2×Dic47⋊C4—24no—
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—22no—
84C47⋊#95—24no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C47⋊#95D418yes—
88C47⋊#95Q814yescomplemented
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2312yes—
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2312yes—
94C2×C4⋊C4×C47—24no—
95C2×C4⋊C4×C47—22no—
96C2×C4⋊C4×C47—24no—
97C2×C4⋊C4×C47—24no—
98C2×C4⋊C4×C47—42no—
99#95×C47—22no—
100#95×C47—24no—
101#95×C47Q814yescomplemented
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—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
115C22×C4×C47—21no—
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×C47C2×D414yes—
125C22×C4×C47C2×D412yes—
126C22×C4×C47C2×D414yes—
127C22×C4×C47C2×Q812yes—
128C22×C4×C47C2×Q812yes—
129C22×C4×C47C2×Q812yes—
130C22×C4×C47C2×Q814yes—
131C22×C4×C47C2×Q814yes—
132C22×Dic47—22no—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—21no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—21no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—21no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47C2×D414yes—
155C22×Dic47C2×D414yes—
156C22×Dic47C2×D412yes—
157C22×Dic47C2×D414yes—
158C22×Dic47C2×D414yes—
159C22×Dic47C2×D412yes—
160C22×Dic47C2×Q812yes—
161C22×Dic47C2×Q814yes—
162C22×Dic47C2×Q814yes—
163C22×Dic47C2×Q814yes—
164C22×Dic47C2×Q812yes—
165C22×Dic47#4112yes—
166C2×Dic94—216no—
167C2×Dic94—48no—
168C2×Dic94—48no—
169C2×Dic94—48no—
170C2×Dic94—48no—
171C2×Dic94—48no—
172C2×Dic94—48no—
173C4⋊C4×C47—28no—
174C4⋊C4×C47—48no—
175C4⋊Dic47—28no—
176C4⋊Dic47—48no—
177C4⋊Dic47—44no—
178Dic47⋊C4—216no—
179Dic47⋊C4—28no—
180Dic47⋊C4—48no—
181Dic47⋊C4—48no—
182Dic47⋊C4—44no—
183Dic47⋊C4—44no—
184C4×Dic47—28no—
185C4×Dic47—216no—
186C23×C47C22×D411yescharacteristic
187C23×C47C22×D412yes—
188C23×C47C22×D412yes—
189C23×C47C22×Q812yes—
190C23×C47C22×Q811yescharacteristic
191C23×C47C22×Q811yescharacteristic
192C23×C47C22×Q811yescharacteristic
193C23×C47C2×#4111yescharacteristic
194C23×C47H(5,𝔽2)11yescharacteristic
195C23×C47H(5,𝔽2)11yescharacteristic
196C23×C472−1+412yes—
197C2×C4×C47—22no—
198C2×C4×C47—24no—
199C2×C4×C47—22no—
200C2×C4×C47—24no—
201C2×C4×C47—24no—
202C2×C4×C47—24no—
203C2×C4×C47—24no—
204C2×C4×C47—24no—
205C2×C4×C47—24no—
206C2×C4×C47—24no—
207C2×C4×C47—24no—
208C2×C4×C47—22no—
209C2×C4×C47—24no—
210C2×C4×C47—24no—
211C2×C4×C47—24no—
212C2×C4×C47—41no—
213C2×C4×C47—42no—
214C2×C4×C47—42no—
215C2×C4×C47—41no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47C4⋊Q814yes—
225C2×C4×C47C4⋊Q818yescomplemented
226C2×Dic47—22no—
227C2×Dic47—24no—
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—24no—
237C2×Dic47—22no—
238C2×Dic47—24no—
239C2×Dic47—24no—
240C2×Dic47—24no—
241C2×Dic47—41no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—41no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47#12014yes—
254C2×Dic47C22⋊Q818yes—
255C2×Dic47C22⋊Q814yes—
256C2×Dic47#12714yes—
257C2×Dic47C4⋊Q814yes—
258C2×Dic47C4⋊Q818yes—
259C2×Dic47C4⋊Q818yescomplemented
260Dic94—432no—
261#15143—471nomaximal, Sylow
262C22×C47C2×#12011yescharacteristic
263C22×C47C2×C22⋊Q811yescharacteristic
264C22×C47C2×C22⋊Q812yes—
265C22×C47C2×#12711yescharacteristic
266C22×C47C2×C4⋊Q811yescharacteristic
267C22×C47C2×C4⋊Q812yes—
268C22×C47C2×C4⋊Q812yes—
269C22×C47C2×C4⋊Q811yescharacteristic
270C22×C47C2×C4⋊Q812yes—
271C22×C47#53511yescharacteristic
272C22×C47#53611yescharacteristic
273C22×C47#54412yes—
274C22×C47#54412yes—
275C22×C47D4212yes—
276C22×C47D4212yes—
277C22×C47#54712yes—
278C22×C47D4×Q812yes—
279C22×C47D4×Q812yes—
280C22×C47D4×Q812yes—
281C22×C47#55411yescharacteristic
282C22×C47#55411yescharacteristic
283C22×C47Q8211yescharacteristic
284C22×C47Q8211yescharacteristic
285C4×C47—24no—
286C4×C47—28no—
287C4×C47—44no—
288C4×C47—42no—
289C4×C47—81no—
290Dic47—24no—
291Dic47—28no—
292Dic47—44no—
293Dic47—42no—
294Dic47—81no—
295Dic47#39518yescomplemented
296C22×C4⋊Q8—471no—
297C2×#395—472no—
298C2×#395—472no—
299C2×#389—471no—
300C2×#384—472no—
301#1444—471no—
302#1444—471no—
303#1444—471no—
304#1444D4711yescharacteristic
305C4⋊#95—472no—
306C4×#95—471no—
307C2×C47C2×#39511yescharacteristic
308C2×C47#243311yescharacteristic
309C2×C47#243411yescharacteristic
310C2×C47#244012yes—
311C2×C47#244012yes—
312C2×C47#254211yescharacteristic
313C2×C47#255112yes—
314C2×C47#255112yes—
315C2×C47#256711yescharacteristic
316C2×C47#266011yescharacteristic
317C2×C47#286811yescharacteristic
318C23×Q8—472no—
319C2×C4⋊Q8—944no—
320C2×C4⋊Q8—948no—
321C22×C4⋊C4—472no—
322C22×C4⋊C4—471no—
323C22×C4⋊C4—471no—
324C22×C4⋊C4—471no—
325C22×C4⋊C4—471no—
326C22×C4⋊C4—471no—
327C22×C4⋊C4—472no—
328C22×C4⋊C4—472no—
329C22×C4⋊C4—472no—
330C22×C4⋊C4C2×D4711yescharacteristic
331C22×C4⋊C4C2×D4712yes—
332C22×C42—471no—
333C22×C42—472no—
334#395—948no—
335#395—948no—
336#389—944no—
337#384—948no—
338C2×#95—472no—
339C2×#95—471no—
340C2×#95—472no—
341C2×#95—472no—
342C2×#95—472no—
343C2×#95—471no—
344C2×#95C2×D4712yes—
345C2×#95C2×D4711yescharacteristic
346C2×#95C2×D4711yescharacteristic
347C47#1514311yescharacteristic, complemented, Sylow
348C22×Q8—944no—
349C22×Q8—944no—
350C22×Q8—944no—
351C22×Q8—944no—
352C22×Q8—944no—
353C22×Q8—1882no—
354C22×Q8—1882no—
355C23×C4—471no—
356C23×C4—471no—
357C23×C4—472no—
358C23×C4—472no—
359C23×C4—471no—
360C23×C4—471no—
361C23×C4C22×D4711yescharacteristic
362C23×C4C22×D4712yes—
363C23×C4C22×D4711yescharacteristic
364C23×C4C22×D4711yescharacteristic
365C23×C4C22×D4712yes—
366C4⋊Q8—9432no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—478no—
373C2×C4⋊C4—474no—
374C2×C4⋊C4—944no—
375C2×C4⋊C4—944no—
376C2×C4⋊C4—944no—
377C2×C4⋊C4—942no—
378C2×C4⋊C4—942no—
379C2×C4⋊C4—942no—
380C2×C4⋊C4—944no—
381C2×C4⋊C4—944no—
382C2×C4⋊C4—942no—
383C2×C4⋊C4—942no—
384C2×C4⋊C4—944no—
385C2×C4⋊C4—944no—
386C2×C4⋊C4—944no—
387C2×C4⋊C4—944no—
388C2×C4⋊C4—942no—
389C2×C4⋊C4—944no—
390C2×C4⋊C4—944no—
391C2×C4⋊C4—944no—
392C2×C4⋊C4—1882no—
393C2×C4⋊C4—1882no—
394C2×C4⋊C4—1882no—
395C2×C42—474no—
396C2×C42—478no—
397C2×C42—944no—
398C2×C42—944no—
399C2×C42—944no—
400#95—22no—
401#95—24no—
402#95—478no—
403#95—474no—
404#95—944no—
405#95—944no—
406#95—942no—
407#95—944no—
408#95Dic9414yescomplemented
409C24C23×D4711yescharacteristic
410C2×Q8—9416no—
411C2×Q8—1888no—
412C2×Q8—1888no—
413C2×Q8—1888no—
414C2×Q8—1888no—
415C2×Q8—1888no—
416C2×Q8—1888no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—472no—
439C22×C4—474no—
440C22×C4—474no—
441C22×C4—472no—
442C22×C4—472no—
443C22×C4—474no—
444C22×C4—474no—
445C22×C4—472no—
446C22×C4—474no—
447C22×C4—474no—
448C22×C4—474no—
449C22×C4—472no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—941no—
454C22×C4—942no—
455C22×C4—941no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—941no—
459C22×C4—942no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—942no—
463C22×C4—941no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—941no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4C2×Dic9412yes—
473C22×C4C2×Dic9414yes—
474C22×C4D4×D4714yes—
475C22×C4D4×D4712yes—
476C22×C4D4×D4714yes—
477C22×C4Q8×D4712yes—
478C22×C4Q8×D4712yes—
479C22×C4Q8×D4714yes—
480C4⋊C4—28no—
481C4⋊C4—48no—
482C4⋊C4—948no—
483C4⋊C4—9416no—
484C4⋊C4—948no—
485C4⋊C4—1888no—
486C4⋊C4—1888no—
487C4⋊C4—1884no—
488C4⋊C4—1884no—
489C4⋊C4—1884no—
490C4⋊C4—1888no—
491C42—9416no—
492C42—948no—
493C23C2×D4×D4712yes—
494C23C2×D4×D4712yes—
495C23C2×D4×D4711yescharacteristic
496C23C2×Q8×D4712yes—
497C23C2×Q8×D4711yescharacteristic
498C23C2×Q8×D4711yescharacteristic
499C23C22×Dic9411yescharacteristic
500C23#41×D4711yescharacteristic
501C23#1309406911yescharacteristic
502C23#1309407011yescharacteristic
503C23#1309407112yes—
504Q8—18832no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—474no—
533C2×C4—478no—
534C2×C4—474no—
535C2×C4—478no—
536C2×C4—474no—
537C2×C4—474no—
538C2×C4—478no—
539C2×C4—944no—
540C2×C4—944no—
541C2×C4—944no—
542C2×C4—944no—
543C2×C4—944no—
544C2×C4—944no—
545C2×C4—944no—
546C2×C4—942no—
547C2×C4—944no—
548C2×C4—942no—
549C2×C4—944no—
550C2×C4—944no—
551C2×C4—944no—
552C2×C4—944no—
553C2×C4—942no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1882no—
560C2×C4—1882no—
561C2×C4—1882no—
562C2×C4—1881no—
563C2×C4—1882no—
564C2×C4—1882no—
565C2×C4—1881no—
566C2×C4#1309402314yes—
567C2×C4#1309402318yescomplemented
568C22#120×D4711yescharacteristic
569C22C22⋊Q8×D4711yescharacteristic
570C22C22⋊Q8×D4712yes—
571C22#127×D4711yescharacteristic
572C22C4⋊Q8×D4712yes—
573C22C4⋊Q8×D4712yes—
574C22C4⋊Q8×D4711yescharacteristic
575C22C2×#1309402311yescharacteristic
576C22C2×#1309402312yes—
577C22#1568968911yescharacteristic
578C22#1568969511yescharacteristic
579C22#1568975212yes—
580C22#1568975312yes—
581C22#1568975512yes—
582C22#1568975712yes—
583C22#1568977112yes—
584C22#1568978612yes—
585C22#1568978612yes—
586C22D4×Dic9412yes—
587C22#1568982911yescharacteristic
588C22#1568983211yescharacteristic
589C22#1568985311yescharacteristic
590C22Q8×Dic9411yescharacteristic
591C4—28no—
592C4—24no—
593C4—42no—
594C4—44no—
595C4—81no—
596C4—478no—
597C4—948no—
598C4—944no—
599C4—3761no—
600C4—1882no—
601C4—1884no—
602C2#395×D4711yescharacteristic
603C2#2024702011yescharacteristic
604C2#2024703011yescharacteristic
605C2#2024708512yes—
606C2#2024708912yes—
607C2#2024833611yescharacteristic
608C2#2024841312yes—
609C2#2024841612yes—
610C2#2024859511yescharacteristic
611C2#2024951111yescharacteristic
612C2#2025178511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, prime radical, cosocleC24×C47C24
FittingC47×#1444C2
hypercenter#1444D47
hypocenterC47#15143
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
77. C2×Dic47⋊C4Q8semidirect
82. C2×C4×Dic47Q8semidirect
88. C47⋊#95Q8semidirect
101. #95×C47Q8semidirect
225. C2×C4×C47C4⋊Q8semidirect
259. C2×Dic47C4⋊Q8semidirect
295. Dic47#395semidirect
347. C47#15143semidirect
408. #95Dic94semidirect
567. C2×C4#13094023semidirect

Maximal subgroups

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

subgroupindex
C22×#130940232
C2×#156890442
C2×#156890432
C2×#156890202
C2×#156889922
#202416532
#202416522
#202416512
Dic47⋊#952
#95×Dic472
C47×#14442
#1514347