Finite Group Databasebeta

← #26233867

Subgroups — #26233867

Order 12032.

780 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689183C211yesmaximal, characteristic
2C2×#15689178C211yesmaximal, characteristic
3#20245868C211yesmaximal, characteristic
4#20244108C211yesmaximal, characteristic, complemented
5#20244105C211yesmaximal, characteristic, complemented
6#20243954C211yesmaximal, characteristic, complemented
7#20243951C211yesmaximal, characteristic, complemented
8#20243946C211yesmaximal, characteristic, complemented
9#20243458C211yesmaximal, characteristic
10#20243455C211yesmaximal, characteristic
11#20243371C211yesmaximal, characteristic
12#20243264C211yesmaximal, characteristic, complemented
13#20243254C211yesmaximal, characteristic, complemented
14#20243153C211yesmaximal, characteristic
15C47×#1917C211yesmaximal, characteristic, complemented
16C2×#13093981C2211yescharacteristic
17C2×#13093981C2211yescharacteristic
18C2×C42×D47C2211yescharacteristic
19#15689183—24no—
20#15689178—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×Dic47⋊C8C2211yescharacteristic
26C2×(C2×D47)⋊C8C2211yescharacteristic
27C2×(C2×D47)⋊C8C2211yescharacteristic
28C2×(C2×D47)⋊C8C2211yescharacteristic
29C2×(C2×D47)⋊C8C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31C2×#13093934C2211yescharacteristic
32C2×#13093934C2211yescharacteristic
33C2×C8×Dic47C2211yescharacteristic
34C2×C8×Dic47C2211yescharacteristic
35#15689020C411yescharacteristic
36#15689020C411yescharacteristic
37#15689018C411yescharacteristic
38#15689018C411yescharacteristic
39#15688997C411yescharacteristic
40#15688997C411yescharacteristic
41#15688994C411yescharacteristic
42#15688994C411yescharacteristic
43C4×Dic47⋊C4C2211yescharacteristic
44C4×Dic47⋊C4C2211yescharacteristic
45C4×C4⋊Dic47C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C2×C4⋊C8×C47C2211yescharacteristic
55C2×#97×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×C4×D47C2×C411yescharacteristic
62C22×C4×D47C2×C411yescharacteristic
63C22×C4×D47C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13093981—22no—
69#13093981—22no—
70#13093981—22no—
71#13093981—22no—
72C2×C4⋊Dic47C2×C411yescharacteristic
73C2×C4⋊Dic47C2×C411yescharacteristic
74C2×Dic47⋊C4C2×C411yescharacteristic
75C2×Dic47⋊C4C2×C411yescharacteristic
76C2×Dic47⋊C4C2×C411yescharacteristic
77C2×Dic47⋊C4C2×C411yescharacteristic
78C2×Dic47⋊C4C2×C411yescharacteristic
79C2×Dic47⋊C4C2×C411yescharacteristic
80C2×Dic47⋊C4C2×C411yescharacteristic
81C2×Dic47⋊C4C2×C411yescharacteristic
82C2×(C2×D47)⋊C4C2×C411yescharacteristic
83C2×(C2×D47)⋊C4C2×C411yescharacteristic
84C2×(C2×D47)⋊C4C2×C411yescharacteristic
85C2×(C2×D47)⋊C4C2×C411yescharacteristic
86C2×C4×Dic47C2×C411yescharacteristic
87C2×C4×Dic47C2×C411yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89C2×C4×Dic47C2311yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91C42×D47—22no—
92C42×D47—22no—
93C4⋊(C47⋊C8)—22no—
94Dic47⋊C8—22no—
95Dic47⋊C8—22no—
96Dic47⋊C8—22no—
97Dic47⋊C8—22no—
98(C2×D47)⋊C8—22no—
99(C2×D47)⋊C8—22no—
100(C2×D47)⋊C8—22no—
101(C2×D47)⋊C8D414yes—
102#13093935—22no—
103#13093934—22no—
104#13093934—22no—
105C8×Dic47—22no—
106C8×Dic47—22no—
107C47⋊#95C2×C411yescharacteristic
108C47⋊#95C2×C411yescharacteristic
109C47⋊#95C2×C411yescharacteristic
110C47⋊#95C2×C411yescharacteristic
111C47⋊#95C2×C411yescharacteristic
112C47⋊#95C2×C411yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2×C411yescharacteristic
118C2×C4⋊C4×C47C2×C411yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121C2×C42×C47C2311yescharacteristic
122C4⋊C8×C47—22no—
123#97×C47—22no—
124#95×C47C2×C411yescharacteristic
125#95×C47C2×C411yescharacteristic
126C23×D47C22×C411yescharacteristic
127C22×C4×C47C22×C411yescharacteristic
128C22×C4×C47C22×C411yescharacteristic
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C22×C411yescharacteristic
131C22×C4×C47C22×C411yescharacteristic
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C2411yescharacteristic
134C22×Dic47C22×C411yescharacteristic
135C22×Dic47C22×C411yescharacteristic
136C22×Dic47C22×C411yescharacteristic
137C22×Dic47C22×C411yescharacteristic
138C22×Dic47C22×C411yescharacteristic
139C22×Dic47C22×C411yescharacteristic
140C22×Dic47C22×C411yescharacteristic
141C2×C4×D47—21no—
142C2×C4×D47—21no—
143C2×C4×D47—21no—
144C2×C4×D47—21no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×C4×D47—41no—
149C2×C4×D47—41no—
150C2×C4×D47—41no—
151C2×C4×D47C2×D412yes—
152C2×C4×D47#4112yes—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47C2×D412yes—
165C4⋊C4×C47—41no—
166C4⋊C4×C47—41no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47—21no—
172C42×C47—21no—
173(C2×D47)⋊C4—22no—
174(C2×D47)⋊C4—22no—
175(C2×D47)⋊C4—22no—
176(C2×D47)⋊C4—22no—
177C4⋊Dic47—22no—
178C4⋊Dic47—41no—
179Dic47⋊C4—22no—
180Dic47⋊C4—22no—
181Dic47⋊C4—22no—
182Dic47⋊C4—22no—
183Dic47⋊C4—22no—
184Dic47⋊C4—41no—
185Dic47⋊C4—41no—
186Dic47⋊C4—41no—
187C4×Dic47—21no—
188C4×Dic47—21no—
189C4×Dic47—21no—
190C4×Dic47—21no—
191C4×Dic47—22no—
192C4×Dic47—22no—
193C4×Dic47#4112yes—
194C4×Dic47#4112yes—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8C2×D412yes—
207C23×C47C23×C411yescharacteristic
208C22×D47—21no—
209C22×D47—21no—
210C22×D47—21no—
211C22×D47—21no—
212C22×D47—21no—
213C22×D47—21no—
214C22×D47C4×D412yes—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×C4×C472−1+411yescharacteristic
238C2×C4×C472−1+411yescharacteristic
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—21no—
243C2×Dic47—21no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—21no—
251C2×Dic47—21no—
252C2×Dic47—21no—
253C2×Dic47—21no—
254C2×Dic47—21no—
255C2×Dic47—21no—
256C2×Dic47#11712yes—
257C2×Dic47#11712yes—
258C2×Dic47C4×D412yes—
259C2×Dic47#13112yes—
260C4×D47—22no—
261C4×D47—22no—
262C4×D47—22no—
263C4×D47—22no—
264C4×D47—44no—
265C4×D47—44no—
266C8×C47—22no—
267C8×C47—41no—
268C8×C47—41no—
269C8×C47—41no—
270C47⋊C8—22no—
271C47⋊C8—41no—
272C47⋊C8—41no—
273C47⋊C8—41no—
274#22605—471nomaximal, Sylow
275C22×C47C2×#11711yescharacteristic
276C22×C47C2×C4×D411yescharacteristic
277C22×C47#51911yescharacteristic
278C22×C47C2×#13111yescharacteristic
279C22×C47#56811yescharacteristic
280C22×C47#56811yescharacteristic
281C22×C47#56811yescharacteristic
282C2×D47—22no—
283C2×D47—22no—
284C2×D47—22no—
285C2×D47—41no—
286C2×D47—41no—
287C2×D47—41no—
288C2×D47—41no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47#54711yescharacteristic
296C4×C47#54711yescharacteristic
297C4×C47#55211yescharacteristic
298C4×C47#55211yescharacteristic
299Dic47—22no—
300Dic47—22no—
301Dic47—22no—
302Dic47—22no—
303Dic47—41no—
304Dic47—41no—
305Dic47—41no—
306C2×#433—471no—
307C2×#432—471no—
308#2296—471no—
309#1940—471no—
310#1939—471no—
311#1917—471no—
312#1917—471no—
313#1917D4711yescharacteristic, complemented
314#1916—471no—
315#1818—471no—
316#1817—471no—
317#1798—471no—
318#1771—471no—
319#1770—471no—
320#1750—471no—
321C2×C47#234411yescharacteristic
322C2×C47#292311yescharacteristic
323C2×C47#292511yescharacteristic
324C2×C47#293011yescharacteristic
325C2×C47#293311yescharacteristic
326C2×C47#298511yescharacteristic
327C2×C47#298711yescharacteristic
328D47—42no—
329C2×#117—471no—
330C2×#117—471no—
331C22×C42—471no—
332#433—944no—
333#432—944no—
334C2×C4⋊C8—471no—
335C2×C4⋊C8—471no—
336C2×C4⋊C8—471no—
337C2×C4⋊C8—471no—
338C2×C4⋊C8—471no—
339C2×C4⋊C8C2×D4711yescharacteristic
340C2×C22⋊C8—471no—
341C2×C22⋊C8—471no—
342C2×C22⋊C8—471no—
343C2×C22⋊C8—471no—
344C2×#97—471no—
345C2×#97—471no—
346C2×#97—471no—
347C2×#97C2×D4711yescharacteristic
348C2×C4×C8—471no—
349C2×C4×C8—471no—
350#389—471no—
351#389—471no—
352#389—471no—
353#389—471no—
354#385—471no—
355#385—471no—
356#385—471no—
357#385—471no—
358C4×C4⋊C4—471no—
359C4×C4⋊C4—471no—
360C4×C4⋊C4—471no—
361C4×C4⋊C4C2×D4711yescharacteristic
362#336—471no—
363#336—471no—
364#336—471no—
365#336—471no—
366#336—471no—
367#336—471no—
368#336—471no—
369#336—471no—
370#336C2×D4711yescharacteristic
371#336C2×D4711yescharacteristic
372#336C2×D4711yescharacteristic
373#336C2×D4711yescharacteristic
374C47#2260511yescharacteristic, complemented, Sylow
375C23×C4—471no—
376C23×C4—471no—
377C23×C4—471no—
378C22×C8—471no—
379C22×C8—471no—
380C22×C8—471no—
381C22×C8—471no—
382C22×C8C22×D4711yescharacteristic
383C22×C8C22×D4711yescharacteristic
384C22×C8C22×D4711yescharacteristic
385C22×C8C22×D4711yescharacteristic
386#117—942no—
387#117—942no—
388#117—942no—
389#117—942no—
390C2×C4⋊C4—471no—
391C2×C4⋊C4—471no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—471no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—471no—
400C2×C4⋊C4C4×D4711yescharacteristic
401C2×C4⋊C4C4×D4711yescharacteristic
402C2×C22⋊C4—471no—
403C2×C22⋊C4—471no—
404C2×C22⋊C4—471no—
405C2×C22⋊C4—471no—
406C2×C42—471no—
407C2×C42—471no—
408C2×C42—471no—
409C2×C42—471no—
410C2×C42—471no—
411C2×C42—942no—
412C2×C42—942no—
413C2×C42C22×D4711yescharacteristic
414C2×C42C22×D4711yescharacteristic
415C2×C42C22×D4711yescharacteristic
416C4⋊C8—22no—
417C4⋊C8—942no—
418C4⋊C8—942no—
419C4⋊C8—942no—
420C4⋊C8—942no—
421C4⋊C8—942no—
422C22⋊C8—474no—
423C22⋊C8—942no—
424C22⋊C8—942no—
425C22⋊C8—942no—
426#97—22no—
427#97—942no—
428#97—942no—
429#97—942no—
430C4×C8—942no—
431C4×C8—942no—
432#95—471no—
433#95—471no—
434#95—471no—
435#95—471no—
436#95—471no—
437#95—471no—
438#95C4×D4711yescharacteristic
439#95C4×D4711yescharacteristic
440C24—471no—
441C22×C4—471no—
442C22×C4—471no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—472no—
446C22×C4—472no—
447C22×C4—471no—
448C22×C4—471no—
449C22×C4—471no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—1881no—
458C22×C4—1881no—
459C22×C4—1881no—
460C22×C4C2×C4×D4711yescharacteristic
461C22×C4C2×C4×D4711yescharacteristic
462C22×C4C2×C4×D4711yescharacteristic
463C22×C4C2×C4×D4711yescharacteristic
464C22×C4C2×C4×D4711yescharacteristic
465C22×C4C2×C4×D4711yescharacteristic
466C22×C4C23×D4711yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—472no—
479C2×C8—941no—
480C2×C8—941no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—941no—
485C2×C8—941no—
486C2×C8—941no—
487C2×C8—941no—
488C2×C8—941no—
489C2×C8—941no—
490C2×C8D4×D4712yes—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—942no—
494C4⋊C4—942no—
495C4⋊C4—942no—
496C4⋊C4—942no—
497C4⋊C4—942no—
498C4⋊C4—942no—
499C4⋊C4—1881no—
500C4⋊C4—1881no—
501C4⋊C4—1881no—
502C4⋊C4—1881no—
503C22⋊C4—942no—
504C22⋊C4—942no—
505C22⋊C4—942no—
506C22⋊C4—942no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—472no—
514C42—472no—
515C42—942no—
516C42—942no—
517C42—941no—
518C42—941no—
519C42—941no—
520C42—941no—
521C23—472no—
522C23—941no—
523C23—941no—
524C23—941no—
525C23—941no—
526C23—941no—
527C23—941no—
528C23C22×C4×D4711yescharacteristic
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—472no—
548C2×C4—472no—
549C2×C4—472no—
550C2×C4—472no—
551C2×C4—941no—
552C2×C4—941no—
553C2×C4—941no—
554C2×C4—941no—
555C2×C4—941no—
556C2×C4—941no—
557C2×C4—941no—
558C2×C4—941no—
559C2×C4—942no—
560C2×C4—942no—
561C2×C4—942no—
562C2×C4—942no—
563C2×C4—941no—
564C2×C4—941no—
565C2×C4—941no—
566C2×C4—941no—
567C2×C4—941no—
568C2×C4—941no—
569C2×C4—941no—
570C2×C4—941no—
571C2×C4—941no—
572C2×C4—1884no—
573C2×C4—1884no—
574C2×C4C2×D4×D4711yescharacteristic
575C2×C4#41×D4711yescharacteristic
576C2×C4#41×D4711yescharacteristic
577C2×C4#41×D4711yescharacteristic
578C2×C4#1309407111yescharacteristic
579C2×C4#1309407211yescharacteristic
580C8—22no—
581C8—41no—
582C8—41no—
583C8—41no—
584C8—942no—
585C8—1881no—
586C8—1881no—
587C8—1881no—
588C22—942no—
589C22—942no—
590C22—942no—
591C22—1881no—
592C22—1881no—
593C22—1881no—
594C22—1881no—
595C22#117×D4711yescharacteristic
596C22C4×D4×D4711yescharacteristic
597C22#1568959911yescharacteristic
598C22#131×D4711yescharacteristic
599C22#1568988811yescharacteristic
600C22#1568988911yescharacteristic
601C22#1568988911yescharacteristic
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—942no—
609C4—942no—
610C4—942no—
611C4—942no—
612C4—1881no—
613C4—1881no—
614C4—1881no—
615C4#1568977111yescharacteristic
616C4#1568977511yescharacteristic
617C4#1568980511yescharacteristic
618C4#1568980911yescharacteristic
619C2—1882no—
620C2#2024625411yescharacteristic
621C2#2025203411yescharacteristic
622C2#2025205111yescharacteristic
623C2#2025208611yescharacteristic
624C2#2025211711yescharacteristic
625C2#2025248111yescharacteristic
626C2#2025249111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1917C2
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1917D47
hypocenterC47#22605
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
4. #20244108C2semidirect
5. #20244105C2semidirect
6. #20243954C2semidirect
7. #20243951C2semidirect
8. #20243946C2semidirect
12. #20243264C2semidirect
13. #20243254C2semidirect
15. C47×#1917C2semidirect
313. #1917D47semidirect
374. C47#22605semidirect

Maximal subgroups

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

subgroupindex
C2×#156891832
C2×#156891782
#202458682
#202441082
#202441052
#202439542
#202439512
#202439462
#202434582
#202434552
#202433712
#202432642
#202432542
#202431532
C47×#19172
#2260547