Finite Group Databasebeta

← #26153002

Subgroups — #26153002

Order 12032.

1566 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689057C212yesmaximal
2C2×#15689056C212yesmaximal
3C2×#15689020C211yesmaximal, characteristic
4C2×#15688992C212yesmaximal
5C2×#15688992C211yesmaximal, characteristic
6#20241653C211yesmaximal, characteristic
7#20241652C211yesmaximal, characteristic
8#20241651C211yesmaximal, characteristic
9Dic47⋊#95C212yesmaximal
10#95×Dic47C211yesmaximal, characteristic
11C47×#1444C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2211yescharacteristic
15C22×Dic47⋊C4C2212yes—
16C22×Dic47⋊C4C2212yes—
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2212yes—
20C22×Dic47⋊C4C2212yes—
21C22×Dic47⋊C4C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2212yes—
24#15689057—28no—
25#15689056—28no—
26#15689020—24no—
27#15688992—28no—
28#15688992—24no—
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2211yescharacteristic
35C22×C4⋊C4×C47C2212yes—
36C22×C4⋊C4×C47C2211yescharacteristic
37C2×#95×C47C2211yescharacteristic
38C2×#95×C47C2212yes—
39C2×#95×C47C2211yescharacteristic
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2312yes—
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2312yes—
45C23×Dic47C2311yescharacteristic
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47—24no—
48C2×C4⋊Dic47—24no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—24no—
51C2×C4⋊Dic47—42no—
52C2×C4⋊Dic47—42no—
53C2×Dic47⋊C4—22no—
54C2×Dic47⋊C4—22no—
55C2×Dic47⋊C4—24no—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4—24no—
58C2×Dic47⋊C4—24no—
59C2×Dic47⋊C4—24no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4—22no—
62C2×Dic47⋊C4—24no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—24no—
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⋊C4D414yes—
72C2×C4×Dic47—24no—
73C2×C4×Dic47—24no—
74C2×C4×Dic47—24no—
75C2×C4×Dic47D414yes—
76C2×C4×Dic47Q818yes—
77C47⋊#95—22no—
78C47⋊#95—24no—
79C47⋊#95—24no—
80C47⋊#95—24no—
81C47⋊#95D418yes—
82C47⋊#95Q814yes—
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2312yes—
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2312yes—
87C23×C4×C47C2311yescharacteristic
88C2×C4⋊C4×C47—24no—
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47—24no—
91C2×C4⋊C4×C47—42no—
92C2×C4⋊C4×C47—42no—
93#95×C47—22no—
94#95×C47—24no—
95#95×C47Q814yes—
96C24×C47C2411yescharacteristic
97C22×C4×C47—22no—
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—21no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47C2×D412yes—
120C22×C4×C47C2×D414yes—
121C22×C4×C47C2×D412yes—
122C22×C4×C47C2×Q814yes—
123C22×C4×C47C2×Q812yes—
124C22×C4×C47C2×Q812yes—
125C22×C4×C47C2×Q814yes—
126C22×Dic47—22no—
127C22×Dic47—22no—
128C22×Dic47—22no—
129C22×Dic47—22no—
130C22×Dic47—21no—
131C22×Dic47—21no—
132C22×Dic47—22no—
133C22×Dic47—21no—
134C22×Dic47—22no—
135C22×Dic47—21no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—21no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47C2×D412yes—
150C22×Dic47C2×D414yes—
151C22×Dic47C2×D412yes—
152C22×Dic47C2×D414yes—
153C22×Dic47C2×D412yes—
154C22×Dic47C2×D412yes—
155C22×Dic47C2×Q814yes—
156C22×Dic47C2×Q814yes—
157C22×Dic47C2×Q814yes—
158C22×Dic47#4112yes—
159C22×Dic47#4114yes—
160C4⋊C4×C47—48no—
161C4⋊C4×C47—44no—
162C4⋊Dic47—48no—
163C4⋊Dic47—44no—
164C4⋊Dic47—44no—
165Dic47⋊C4—28no—
166Dic47⋊C4—48no—
167Dic47⋊C4—48no—
168Dic47⋊C4—48no—
169Dic47⋊C4—44no—
170Dic47⋊C4—44no—
171Dic47⋊C4—48no—
172C4×Dic47—216no—
173C4×Dic47—28no—
174C23×C47C22×D411yescharacteristic
175C23×C47C22×D411yescharacteristic
176C23×C47C22×D412yes—
177C23×C47C22×Q812yes—
178C23×C47C22×Q811yescharacteristic
179C23×C47C22×Q811yescharacteristic
180C23×C47C2×#4111yescharacteristic
181C23×C47C2×#4112yes—
182C23×C47H(5,𝔽2)12yes—
183C23×C472−1+411yescharacteristic
184C23×C472−1+411yescharacteristic
185C2×C4×C47—24no—
186C2×C4×C47—22no—
187C2×C4×C47—22no—
188C2×C4×C47—24no—
189C2×C4×C47—24no—
190C2×C4×C47—24no—
191C2×C4×C47—24no—
192C2×C4×C47—24no—
193C2×C4×C47—24no—
194C2×C4×C47—24no—
195C2×C4×C47—22no—
196C2×C4×C47—24no—
197C2×C4×C47—41no—
198C2×C4×C47—41no—
199C2×C4×C47—42no—
200C2×C4×C47—42no—
201C2×C4×C47—41no—
202C2×C4×C47—41no—
203C2×C4×C47—42no—
204C2×C4×C47—42no—
205C2×C4×C47—41no—
206C2×C4×C47—42no—
207C2×C4×C47—42no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47C4⋊Q818yes—
213C2×C4×C47C4⋊Q814yes—
214C2×Dic47—24no—
215C2×Dic47—22no—
216C2×Dic47—22no—
217C2×Dic47—24no—
218C2×Dic47—24no—
219C2×Dic47—24no—
220C2×Dic47—24no—
221C2×Dic47—24no—
222C2×Dic47—24no—
223C2×Dic47—24no—
224C2×Dic47—22no—
225C2×Dic47—24no—
226C2×Dic47—41no—
227C2×Dic47—41no—
228C2×Dic47—42no—
229C2×Dic47—42no—
230C2×Dic47—41no—
231C2×Dic47—42no—
232C2×Dic47—41no—
233C2×Dic47—42no—
234C2×Dic47—41no—
235C2×Dic47—42no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47#12114yes—
242C2×Dic47C22⋊Q818yes—
243C2×Dic47#12314yes—
244C2×Dic47#12518yes—
245C2×Dic47#12714yes—
246C2×Dic47C4⋊Q818yes—
247C2×Dic47C4⋊Q814yes—
248#15145—471nomaximal, Sylow
249C22×C47C2×#12111yescharacteristic
250C22×C47C2×C22⋊Q812yes—
251C22×C47C2×#12311yescharacteristic
252C22×C47C2×#12512yes—
253C22×C47C2×#12711yescharacteristic
254C22×C47C2×C4⋊Q811yescharacteristic
255C22×C47C2×C4⋊Q812yes—
256C22×C47C2×C4⋊Q812yes—
257C22×C47C2×C4⋊Q811yescharacteristic
258C22×C47#53511yescharacteristic
259C22×C47#53611yescharacteristic
260C22×C47#54412yes—
261C22×C47#54412yes—
262C22×C47D4212yes—
263C22×C47#54712yes—
264C22×C47#54712yes—
265C22×C47D4×Q811yescharacteristic
266C22×C47D4×Q811yescharacteristic
267C22×C47#55012yes—
268C22×C47#55412yes—
269C22×C47#55412yes—
270C22×C47#55711yescharacteristic
271C22×C47#55711yescharacteristic
272C4×C47—28no—
273C4×C47—24no—
274C4×C47—42no—
275C4×C47—81no—
276C4×C47—82no—
277Dic47—28no—
278Dic47—24no—
279Dic47—42no—
280Dic47—81no—
281Dic47—82no—
282Dic47#39818yescomplemented
283C2×#398—472no—
284C2×#398—472no—
285C2×#389—471no—
286C2×#384—472no—
287C2×#384—471no—
288#1444—471no—
289#1444—471no—
290#1444—471no—
291#1444D4711yescharacteristic
292C4⋊#95—472no—
293C4×#95—471no—
294C2×C47C2×#39811yescharacteristic
295C2×C47#244012yes—
296C2×C47#244012yes—
297C2×C47#250111yescharacteristic
298C2×C47#250211yescharacteristic
299C2×C47#254111yescharacteristic
300C2×C47#254611yescharacteristic
301C2×C47#255212yes—
302C2×C47#255212yes—
303C2×C47#266011yescharacteristic
304C2×C47#286811yescharacteristic
305C22×C4⋊C4—471no—
306C22×C4⋊C4—472no—
307C22×C4⋊C4—471no—
308C22×C4⋊C4—471no—
309C22×C4⋊C4—471no—
310C22×C4⋊C4—472no—
311C22×C4⋊C4—472no—
312C22×C4⋊C4—472no—
313C22×C4⋊C4—472no—
314C22×C4⋊C4—471no—
315C22×C4⋊C4C2×D4712yes—
316C22×C4⋊C4C2×D4711yescharacteristic
317C22×C42—472no—
318C22×C42—471no—
319#398—948no—
320#398—948no—
321#389—944no—
322#384—944no—
323#384—948no—
324C2×#95—472no—
325C2×#95—471no—
326C2×#95—472no—
327C2×#95—472no—
328C2×#95—472no—
329C2×#95—471no—
330C2×#95C2×D4712yes—
331C2×#95C2×D4711yescharacteristic
332C2×#95C2×D4711yescharacteristic
333C47#1514511yescharacteristic, complemented, Sylow
334C23×C4—471no—
335C23×C4—471no—
336C23×C4—472no—
337C23×C4—471no—
338C23×C4—472no—
339C23×C4—471no—
340C23×C4C22×D4712yes—
341C23×C4C22×D4711yescharacteristic
342C23×C4C22×D4711yescharacteristic
343C23×C4C22×D4712yes—
344C23×C4C22×D4711yescharacteristic
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—474no—
351C2×C4⋊C4—942no—
352C2×C4⋊C4—942no—
353C2×C4⋊C4—944no—
354C2×C4⋊C4—944no—
355C2×C4⋊C4—944no—
356C2×C4⋊C4—944no—
357C2×C4⋊C4—944no—
358C2×C4⋊C4—944no—
359C2×C4⋊C4—942no—
360C2×C4⋊C4—942no—
361C2×C4⋊C4—944no—
362C2×C4⋊C4—944no—
363C2×C4⋊C4—944no—
364C2×C4⋊C4—944no—
365C2×C4⋊C4—944no—
366C2×C4⋊C4—944no—
367C2×C4⋊C4—942no—
368C2×C4⋊C4—944no—
369C2×C4⋊C4—944no—
370C2×C4⋊C4—942no—
371C2×C4⋊C4—944no—
372C2×C4⋊C4—1882no—
373C2×C4⋊C4—1882no—
374C2×C4⋊C4—1882no—
375C2×C4⋊C4—1882no—
376C2×C42—474no—
377C2×C42—478no—
378C2×C42—944no—
379C2×C42—944no—
380C2×C42—944no—
381#95—22no—
382#95—24no—
383#95—478no—
384#95—474no—
385#95—944no—
386#95—944no—
387#95—942no—
388#95—944no—
389#95Dic9414yes—
390C24C23×D4711yescharacteristic
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—472no—
414C22×C4—472no—
415C22×C4—474no—
416C22×C4—474no—
417C22×C4—472no—
418C22×C4—474no—
419C22×C4—474no—
420C22×C4—472no—
421C22×C4—474no—
422C22×C4—474no—
423C22×C4—472no—
424C22×C4—942no—
425C22×C4—942no—
426C22×C4—942no—
427C22×C4—942no—
428C22×C4—941no—
429C22×C4—942no—
430C22×C4—941no—
431C22×C4—941no—
432C22×C4—942no—
433C22×C4—941no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4—942no—
437C22×C4—942no—
438C22×C4—941no—
439C22×C4—942no—
440C22×C4—942no—
441C22×C4—942no—
442C22×C4—942no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4C2×Dic9414yes—
448C22×C4C2×Dic9412yes—
449C22×C4D4×D4712yes—
450C22×C4D4×D4714yes—
451C22×C4D4×D4712yes—
452C22×C4Q8×D4712yes—
453C22×C4Q8×D4714yes—
454C4⋊C4—48no—
455C4⋊C4—44no—
456C4⋊C4—948no—
457C4⋊C4—1888no—
458C4⋊C4—1888no—
459C4⋊C4—1884no—
460C4⋊C4—1888no—
461C4⋊C4—1884no—
462C4⋊C4—1888no—
463C4⋊C4—1884no—
464C4⋊C4—1884no—
465C4⋊C4—1888no—
466C42—9416no—
467C42—948no—
468C23C2×D4×D4711yescharacteristic
469C23C2×D4×D4712yes—
470C23C2×D4×D4711yescharacteristic
471C23C2×Q8×D4712yes—
472C23C2×Q8×D4711yescharacteristic
473C23C22×Dic9411yescharacteristic
474C23#41×D4712yes—
475C23#41×D4711yescharacteristic
476C23#1309406912yes—
477C23#1309407111yescharacteristic
478C23#1309407211yescharacteristic
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—474no—
507C2×C4—478no—
508C2×C4—474no—
509C2×C4—478no—
510C2×C4—474no—
511C2×C4—474no—
512C2×C4—478no—
513C2×C4—944no—
514C2×C4—944no—
515C2×C4—944no—
516C2×C4—944no—
517C2×C4—944no—
518C2×C4—944no—
519C2×C4—944no—
520C2×C4—944no—
521C2×C4—942no—
522C2×C4—942no—
523C2×C4—944no—
524C2×C4—942no—
525C2×C4—1882no—
526C2×C4—1882no—
527C2×C4—1882no—
528C2×C4—1882no—
529C2×C4—1882no—
530C2×C4—1882no—
531C2×C4—1882no—
532C2×C4—1881no—
533C2×C4—1882no—
534C2×C4—1881no—
535C2×C4—1882no—
536C2×C4—1881no—
537C2×C4—1882no—
538C2×C4—1881no—
539C2×C4—1881no—
540C2×C4#1309402318yes—
541C2×C4#1309402314yes—
542C22#121×D4711yescharacteristic
543C22C22⋊Q8×D4712yes—
544C22#123×D4711yescharacteristic
545C22#125×D4712yes—
546C22#127×D4711yescharacteristic
547C22C4⋊Q8×D4712yes—
548C22C4⋊Q8×D4711yescharacteristic
549C22C2×#1309402312yes—
550C22C2×#1309402311yescharacteristic
551C22#1568968811yescharacteristic
552C22#1568969611yescharacteristic
553C22#1568975012yes—
554C22#1568975212yes—
555C22#1568975512yes—
556C22#1568977112yes—
557C22#1568977512yes—
558C22#1568978811yescharacteristic
559C22D4×Dic9411yescharacteristic
560C22#1568979112yes—
561C22#1568982712yes—
562C22#1568983212yes—
563C22#1568984911yescharacteristic
564C22#1568985011yescharacteristic
565C4—28no—
566C4—24no—
567C4—42no—
568C4—82no—
569C4—81no—
570C4—478no—
571C4—948no—
572C4—944no—
573C4—3762no—
574C4—3761no—
575C4—1882no—
576C2#398×D4711yescharacteristic
577C2#2024708312yes—
578C2#2024708912yes—
579C2#2024785411yescharacteristic
580C2#2024786411yescharacteristic
581C2#2024832911yescharacteristic
582C2#2024837511yescharacteristic
583C2#2024841812yes—
584C2#2024842512yes—
585C2#2024950611yescharacteristic
586C2#2025178511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, prime radical, cosocleC24×C47C24
FittingC47×#1444C2
hypercenter#1444D47
hypocenterC47#15145
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
282. Dic47#398semidirect
333. C47#15145semidirect

Maximal subgroups

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

subgroupindex
C2×#156890572
C2×#156890562
C2×#156890202
C2×#156889922
#202416532
#202416522
#202416512
Dic47⋊#952
#95×Dic472
C47×#14442
#1514547